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((y-9)/(y-8))*((y^2-64)/(y^2-16*y+64))
(z-(5*z)/z+1)/(z-4)/(z+1)
(s+3)/(5*s+15)
c^(k+5)*c^k/(c^2)^k
Factorizar el polinomio:
y^3+y
y^3+4^3
z^3-5*z^2+9*z-45
y^3-3*y+3^3
Descomponer al cuadrado:
-y^4+8*y^2+2
-y^4+8*y^2+9
-y^4-7*y^2-9
y^4-7*y^2+4
Expresiones idénticas
tan4acot4a-(uno -cos^ dos *9a)/(sin^ dos *9a- uno)
tangente de 4 arcoco tangente de gente de 4a menos (1 menos coseno de al cuadrado multiplicar por 9a) dividir por ( seno de al cuadrado multiplicar por 9a menos 1)
tangente de 4 arcoco tangente de gente de 4a menos (uno menos coseno de en el grado dos multiplicar por 9a) dividir por ( seno de en el grado dos multiplicar por 9a menos uno)
tan4acot4a-(1-cos2*9a)/(sin2*9a-1)
tan4acot4a-1-cos2*9a/sin2*9a-1
tan4acot4a-(1-cos²*9a)/(sin²*9a-1)
tan4acot4a-(1-cos en el grado 2*9a)/(sin en el grado 2*9a-1)
tan4acot4a-(1-cos^29a)/(sin^29a-1)
tan4acot4a-(1-cos29a)/(sin29a-1)
tan4acot4a-1-cos29a/sin29a-1
tan4acot4a-1-cos^29a/sin^29a-1
tan4acot4a-(1-cos^2*9a) dividir por (sin^2*9a-1)
Expresiones semejantes
tan4acot4a-(1-cos^2*9a)/(sin^2*9a+1)
tan4acot4a-(1+cos^2*9a)/(sin^2*9a-1)
tan4acot4a+(1-cos^2*9a)/(sin^2*9a-1)
Expresiones con funciones
Coseno cos
cos(2*t)*x/(cos(t)+sin(x))-cos(t)
cos(x)/(x^2+cos(x))+(-2*x+sin(x))*sin(x)/(x^2+cos(x))^2
cos(x)^atan(x)*(log(cos(x))/(1+x^2)-atan(x)*sin(x)/cos(x))
cos(x)*exp(sin(x))/(x+sin(x))+(-1-cos(x))*(e^sin(x)-1)/(x+sin(x))^2
cos(x)/cos(2*x)+x/(2*(1+x^2/4))+2*sin(x)*sin(2*x)/cos(2*x)^2+atan(x/2)
Seno sin
sin(x+y)/((sin(x)*sin(y)))
sin(x)/(tg(pi/4+x/2)*(1+sin(x)))
sin(x)/(x-sin(x))+(-1+cos(x))*(2-cos(x))/(x-sin(x))^2
sin(x)*(sin(x)/(1-cos(x))-1/tan(x))
sin(x)^(sqrt(x))*(log(sin(x))/(2*sqrt(x))+sqrt(x)*cos(x)/sin(x))

Simplificación de expresiones/ Descomposición en fracciones simples/ tan4acot4a-(1-cos^2*9a)/(sin^2*9a-1)

¿Cómo vas a descomponer esta tan4acot4a-(1-cos^29a)/(sin^29a-1) expresión en fracciones?

Solución

Ha introducido [src]

                          2     
                   1 - cos (9)*a
tan(4*acot(4*a)) - -------------
                      2         
                   sin (9)*a - 1

\tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

tan(4*acot(4*a)) - (1 - cos(9)^2*a)/(sin(9)^2*a - 1)

Simplificación general [src]

          2      /          2   \                 
-1 + a*cos (9) + \-1 + a*sin (9)/*tan(4*acot(4*a))
--------------------------------------------------
                            2                     
                  -1 + a*sin (9)

\frac{a \cos^{2}{\left(9 \right)} + \left(a \sin^{2}{\left(9 \right)} - 1\right) \tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1}

(-1 + a*cos(9)^2 + (-1 + a*sin(9)^2)*tan(4*acot(4*a)))/(-1 + a*sin(9)^2)

Abrimos la expresión [src]

                                                                                                                                                                                                                                                                                                              12                                                                                                                                                                           16                                                                                                                                                                            8                                                                                                                                                                           4                                                                                                                                                                           2                                                                                                                                                                             6                                                                                                                                                                            18                                                                                                                                                                           10                                                                                                                                                                           14                                                                                
       1                    1                                                                                                1                                                                                                                                                                    559104*a*cos  (1)                                                                                                                                                            294912*a*cos  (1)                                                                                                                                                             114048*a*cos (1)                                                                                                                                                              2160*a*cos (1)                                                                                                                                                                81*a*cos (1)                                                                                                                                                               22176*a*cos (1)                                                                                                                                                              65536*a*cos  (1)                                                                                                                                                            329472*a*cos  (1)                                                                                                                                                            552960*a*cos  (1)                                                                             
---------------- - ------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     3      1                 3    1                      12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14                       12                  16                  8                4              2                 6                 18                  10                  14   
a - --- + ------   -6*a + 16*a  + ----   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)   -1 - 559104*a*sin  (1) - 294912*a*sin  (1) - 114048*a*sin (1) - 2160*a*sin (1) + 81*a*sin (1) + 22176*a*sin (1) + 65536*a*sin  (1) + 329472*a*sin  (1) + 552960*a*sin  (1)
    8*a        3                  16*a                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
          256*a

- \frac{114048 a \cos^{8}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} - \frac{559104 a \cos^{12}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} - \frac{2160 a \cos^{4}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} - \frac{294912 a \cos^{16}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} + \frac{65536 a \cos^{18}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} + \frac{81 a \cos^{2}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} + \frac{552960 a \cos^{14}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} + \frac{22176 a \cos^{6}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} + \frac{329472 a \cos^{10}{\left(1 \right)}}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} - \frac{1}{- 559104 a \sin^{12}{\left(1 \right)} - 114048 a \sin^{8}{\left(1 \right)} - 294912 a \sin^{16}{\left(1 \right)} - 2160 a \sin^{4}{\left(1 \right)} + 81 a \sin^{2}{\left(1 \right)} + 65536 a \sin^{18}{\left(1 \right)} + 22176 a \sin^{6}{\left(1 \right)} + 552960 a \sin^{14}{\left(1 \right)} + 329472 a \sin^{10}{\left(1 \right)} - 1} - \frac{1}{16 a^{3} - 6 a + \frac{1}{16 a}} + \frac{1}{a - \frac{3}{8 a} + \frac{1}{256 a^{3}}}

1/(a - 3/(8*a) + 1/(256*a^3)) - 1/(-6*a + 16*a^3 + 1/(16*a)) - 1/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) - 559104*a*cos(1)^12/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) - 294912*a*cos(1)^16/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) - 114048*a*cos(1)^8/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) - 2160*a*cos(1)^4/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) + 81*a*cos(1)^2/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) + 22176*a*cos(1)^6/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) + 65536*a*cos(1)^18/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) + 329472*a*cos(1)^10/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14) + 552960*a*cos(1)^14/(-1 - 559104*a*sin(1)^12 - 294912*a*sin(1)^16 - 114048*a*sin(1)^8 - 2160*a*sin(1)^4 + 81*a*sin(1)^2 + 22176*a*sin(1)^6 + 65536*a*sin(1)^18 + 329472*a*sin(1)^10 + 552960*a*sin(1)^14)

Combinatoria [src]

                             2           2                    
-1 - tan(4*acot(4*a)) + a*cos (9) + a*sin (9)*tan(4*acot(4*a))
--------------------------------------------------------------
                                  2                           
                        -1 + a*sin (9)

\frac{a \sin^{2}{\left(9 \right)} \tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} + a \cos^{2}{\left(9 \right)} - \tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1}

(-1 - tan(4*acot(4*a)) + a*cos(9)^2 + a*sin(9)^2*tan(4*acot(4*a)))/(-1 + a*sin(9)^2)

Denominador racional [src]

          2      /          2   \                 
-1 + a*cos (9) + \-1 + a*sin (9)/*tan(4*acot(4*a))
--------------------------------------------------
                            2                     
                  -1 + a*sin (9)

\frac{a \cos^{2}{\left(9 \right)} + \left(a \sin^{2}{\left(9 \right)} - 1\right) \tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1}

(-1 + a*cos(9)^2 + (-1 + a*sin(9)^2)*tan(4*acot(4*a)))/(-1 + a*sin(9)^2)

Unión de expresiones racionales [src]

          2      /          2   \                 
-1 + a*cos (9) + \-1 + a*sin (9)/*tan(4*acot(4*a))
--------------------------------------------------
                            2                     
                  -1 + a*sin (9)

\frac{a \cos^{2}{\left(9 \right)} + \left(a \sin^{2}{\left(9 \right)} - 1\right) \tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1}

(-1 + a*cos(9)^2 + (-1 + a*sin(9)^2)*tan(4*acot(4*a)))/(-1 + a*sin(9)^2)

Potencias [src]

                       2                                           
         / -9*I    9*I\                                            
         |e       e   |                                            
   1 - a*|----- + ----|        /   4*I*acot(4*a)    -4*I*acot(4*a)\
         \  2      2  /      I*\- e              + e              /
- ------------------------ + --------------------------------------
                         2       -4*I*acot(4*a)    4*I*acot(4*a)   
         /   -9*I    9*I\       e               + e                
       a*\- e     + e   /                                          
  -1 - -------------------                                         
                4

- \frac{- a \left(\frac{e^{- 9 i}}{2} + \frac{e^{9 i}}{2}\right)^{2} + 1}{- \frac{a \left(e^{9 i} - e^{- 9 i}\right)^{2}}{4} - 1} + \frac{i \left(- e^{4 i \operatorname{acot}{\left(4 a \right)}} + e^{- 4 i \operatorname{acot}{\left(4 a \right)}}\right)}{e^{4 i \operatorname{acot}{\left(4 a \right)}} + e^{- 4 i \operatorname{acot}{\left(4 a \right)}}}

          2                      
-1 + a*cos (9)                   
-------------- + tan(4*acot(4*a))
          2                      
-1 + a*sin (9)

\tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} + \frac{a \cos^{2}{\left(9 \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1}

(-1 + a*cos(9)^2)/(-1 + a*sin(9)^2) + tan(4*acot(4*a))

Respuesta numérica [src]

-(1.0 - 0.83015835412204*a)/(-1.0 + 0.16984164587796*a) + tan(4*acot(4*a))

-(1.0 - 0.83015835412204*a)/(-1.0 + 0.16984164587796*a) + tan(4*acot(4*a))

Denominador común [src]

          2                      
-1 + a*cos (9)                   
-------------- + tan(4*acot(4*a))
          2                      
-1 + a*sin (9)

\tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} + \frac{a \cos^{2}{\left(9 \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1}

(-1 + a*cos(9)^2)/(-1 + a*sin(9)^2) + tan(4*acot(4*a))

Parte trigonométrica [src]

           2/    pi\                           2      
  1 - a*sin |9 + --|               /         2\       
            \    2 /          16*a*\-1 + 16*a /       
- ------------------ + -------------------------------
              2                   4        2         6
    -1 + a*sin (9)     -1 - 1792*a  + 112*a  + 4096*a

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{- a \sin^{2}{\left(\frac{\pi}{2} + 9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

   /              pi\                     
cos|4*acot(4*a) - --|                     
   \              2 /   -2 + a + a*cos(18)
--------------------- - ------------------
   cos(4*acot(4*a))     2 - a + a*cos(18)

\frac{\cos{\left(4 \operatorname{acot}{\left(4 a \right)} - \frac{\pi}{2} \right)}}{\cos{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{a \cos{\left(18 \right)} + a - 2}{- a + a \cos{\left(18 \right)} + 2}

                          a    
                   1 - ------- 
                          2    
sec(4*acot(4*a))       sec (9) 
---------------- - ------------
csc(4*acot(4*a))           a   
                   -1 + -------
                           2   
                        csc (9)

\frac{\sec{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\csc{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{- \frac{a}{\sec^{2}{\left(9 \right)}} + 1}{\frac{a}{\csc^{2}{\left(9 \right)}} - 1}

                            2                                    
           /         4     \                                     
           |    4*sin (9/2)|                                     
         a*|1 - -----------|                                     
           |         2     |                                     
           \      sin (9)  /                                     
     1 - --------------------                                    
                           2                                     
          /         4     \                                      
          |    4*sin (9/2)|                                      
          |1 + -----------|                               2      
          |         2     |                   /         2\       
          \      sin (9)  /              16*a*\-1 + 16*a /       
- ----------------------------- + -------------------------------
                2       4                    4        2         6
        16*a*sin (9)*sin (9/2)    -1 - 1792*a  + 112*a  + 4096*a 
  -1 + ------------------------                                  
                              2                                  
       /   2           4     \                                   
       \sin (9) + 4*sin (9/2)/

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{- \frac{a \left(- \frac{4 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}} + 1\right)^{2}}{\left(1 + \frac{4 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}}\right)^{2}} + 1}{\frac{16 a \sin^{4}{\left(\frac{9}{2} \right)} \sin^{2}{\left(9 \right)}}{\left(\sin^{2}{\left(9 \right)} + 4 \sin^{4}{\left(\frac{9}{2} \right)}\right)^{2}} - 1}

               3              2    
  -16*a + 256*a      1 - a*cos (9) 
------------------ - --------------
        2        4             2   
1 - 96*a  + 256*a    -1 + a*sin (9)

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

                             2                         
            /         4     \                          
            |    4*sin (9/2)|                          
          a*|1 - -----------|                          
            |         2     |                          
            \      sin (9)  /                          
      1 - --------------------                         
                            2                          
           /         4     \                           
           |    4*sin (9/2)|                           
           |1 + -----------|                           
           |         2     |             2             
           \      sin (9)  /        2*sin (4*acot(4*a))
- ------------------------------- + -------------------
                     4                sin(8*acot(4*a)) 
             16*a*sin (9/2)                            
  -1 + --------------------------                      
                        2                              
       /         4     \                               
       |    4*sin (9/2)|     2                         
       |1 + -----------| *sin (9)                      
       |         2     |                               
       \      sin (9)  /

- \frac{- \frac{a \left(- \frac{4 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}} + 1\right)^{2}}{\left(1 + \frac{4 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}}\right)^{2}} + 1}{\frac{16 a \sin^{4}{\left(\frac{9}{2} \right)}}{\left(1 + \frac{4 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}}\right)^{2} \sin^{2}{\left(9 \right)}} - 1} + \frac{2 \sin^{2}{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\sin{\left(8 \operatorname{acot}{\left(4 a \right)} \right)}}

                                                      2     
                                  /       2/  9   pi\\      
                                  |    csc |- - + --||      
                                  |        \  2   2 /|      
                                a*|1 - --------------|      
                                  |         2        |      
                                  \      csc (9/2)   /      
                            1 - -----------------------     
                                                     2      
                                 /       2/  9   pi\\       
                                 |    csc |- - + --||       
                                 |        \  2   2 /|       
   /pi              \            |1 + --------------|       
csc|-- - 4*acot(4*a)|            |         2        |       
   \2               /            \      csc (9/2)   /       
--------------------- - ------------------------------------
   csc(4*acot(4*a))                        2/  9   pi\      
                                    4*a*csc |- - + --|      
                                            \  2   2 /      
                        -1 + -------------------------------
                                                 2          
                             /       2/  9   pi\\           
                             |    csc |- - + --||           
                             |        \  2   2 /|     2     
                             |1 + --------------| *csc (9/2)
                             |         2        |           
                             \      csc (9/2)   /

- \frac{- \frac{a \left(- \frac{\csc^{2}{\left(- \frac{9}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{9}{2} \right)}} + 1\right)^{2}}{\left(1 + \frac{\csc^{2}{\left(- \frac{9}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{9}{2} \right)}}\right)^{2}} + 1}{\frac{4 a \csc^{2}{\left(- \frac{9}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{9}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{9}{2} \right)}}\right)^{2} \csc^{2}{\left(\frac{9}{2} \right)}} - 1} + \frac{\csc{\left(- 4 \operatorname{acot}{\left(4 a \right)} + \frac{\pi}{2} \right)}}{\csc{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}

                                               2      
                                   /         2\       
  -2 + a + a*cos(18)          16*a*\-1 + 16*a /       
- ------------------ + -------------------------------
  2 - a + a*cos(18)               4        2         6
                       -1 - 1792*a  + 112*a  + 4096*a

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{a \cos{\left(18 \right)} + a - 2}{- a + a \cos{\left(18 \right)} + 2}

           2            /         2\ 
  1 - a*cos (9)    16*a*\-1 + 16*a / 
- -------------- + ------------------
            2              2        4
  -1 + a*sin (9)   1 - 96*a  + 256*a

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

                              /        2   \
                            a*\-1 + cot (9)/
                   -2 + a + ----------------
                                     2      
       1                      1 + cot (9)   
---------------- - -------------------------
cot(4*acot(4*a))              /        2   \
                            a*\-1 + cot (9)/
                    2 - a + ----------------
                                     2      
                              1 + cot (9)

\frac{1}{\cot{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{\frac{a \left(-1 + \cot^{2}{\left(9 \right)}\right)}{1 + \cot^{2}{\left(9 \right)}} + a - 2}{- a + \frac{a \left(-1 + \cot^{2}{\left(9 \right)}\right)}{1 + \cot^{2}{\left(9 \right)}} + 2}

                                                    2     
                                  /       2/9   pi\\      
                                  |    cos |- - --||      
                                  |        \2   2 /|      
                                a*|1 - ------------|      
                                  |        2       |      
                                  \     cos (9/2)  /      
                            1 - ---------------------     
                                                   2      
                                 /       2/9   pi\\       
                                 |    cos |- - --||       
                                 |        \2   2 /|       
   /              pi\            |1 + ------------|       
cos|4*acot(4*a) - --|            |        2       |       
   \              2 /            \     cos (9/2)  /       
--------------------- - ----------------------------------
   cos(4*acot(4*a))                        2/9   pi\      
                                    4*a*cos |- - --|      
                                            \2   2 /      
                        -1 + -----------------------------
                                               2          
                             /       2/9   pi\\           
                             |    cos |- - --||           
                             |        \2   2 /|     2     
                             |1 + ------------| *cos (9/2)
                             |        2       |           
                             \     cos (9/2)  /

- \frac{- \frac{a \left(- \frac{\cos^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{9}{2} \right)}} + 1\right)^{2}}{\left(1 + \frac{\cos^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{9}{2} \right)}}\right)^{2}} + 1}{\frac{4 a \cos^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{9}{2} \right)}}\right)^{2} \cos^{2}{\left(\frac{9}{2} \right)}} - 1} + \frac{\cos{\left(4 \operatorname{acot}{\left(4 a \right)} - \frac{\pi}{2} \right)}}{\cos{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}

             /       2   \                   
           a*\1 - tan (9)/                   
  -2 + a + ---------------                   
                    2                        
             1 + tan (9)                     
- ------------------------ + tan(4*acot(4*a))
            /       2   \                    
          a*\1 - tan (9)/                    
  2 - a + ---------------                    
                   2                         
            1 + tan (9)

\tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} - \frac{\frac{a \left(1 - \tan^{2}{\left(9 \right)}\right)}{\tan^{2}{\left(9 \right)} + 1} + a - 2}{- a + \frac{a \left(1 - \tan^{2}{\left(9 \right)}\right)}{\tan^{2}{\left(9 \right)} + 1} + 2}

                        2                     
        /        2     \                      
      a*\-1 + cot (9/2)/                      
  1 - -------------------                     
                       2                      
        /       2     \          /         2\ 
        \1 + cot (9/2)/     16*a*\-1 + 16*a / 
- ----------------------- + ------------------
                2                   2        4
         4*a*cot (9/2)      1 - 96*a  + 256*a 
   -1 + ----------------                      
                       2                      
        /       2     \                       
        \1 + cot (9/2)/

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{- \frac{a \left(-1 + \cot^{2}{\left(\frac{9}{2} \right)}\right)^{2}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} + 1}{\frac{4 a \cot^{2}{\left(\frac{9}{2} \right)}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} - 1}

                              2/    pi\
               3     1 - a*sin |9 + --|
  -16*a + 256*a                \    2 /
------------------ - ------------------
        2        4               2     
1 - 96*a  + 256*a      -1 + a*sin (9)

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{- a \sin^{2}{\left(\frac{\pi}{2} + 9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

                               a      
                     1 - -------------
                            2/     pi\
               3         csc |-9 + --|
  -16*a + 256*a              \     2 /
------------------ - -----------------
        2        4              a     
1 - 96*a  + 256*a       -1 + -------  
                                2     
                             csc (9)

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{- \frac{a}{\csc^{2}{\left(-9 + \frac{\pi}{2} \right)}} + 1}{\frac{a}{\csc^{2}{\left(9 \right)}} - 1}

                       2                                  
        /       2     \                                   
      a*\1 - tan (9/2)/                                   
  1 - ------------------                                  
                      2                            2      
       /       2     \                 /         2\       
       \1 + tan (9/2)/            16*a*\-1 + 16*a /       
- ---------------------- + -------------------------------
               2                      4        2         6
        4*a*tan (9/2)      -1 - 1792*a  + 112*a  + 4096*a 
  -1 + ----------------                                   
                      2                                   
       /       2     \                                    
       \1 + tan (9/2)/

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{- \frac{a \left(1 - \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} + 1}{\frac{4 a \tan^{2}{\left(\frac{9}{2} \right)}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} - 1}

              2              /         2\ 
     1 - a*cos (9)      16*a*\-1 + 16*a / 
- ------------------- + ------------------
            2/    pi\           2        4
  -1 + a*cos |9 - --|   1 - 96*a  + 256*a 
             \    2 /

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \cos^{2}{\left(9 - \frac{\pi}{2} \right)} - 1}

                                                2      
              2                     /         2\       
     1 - a*cos (9)             16*a*\-1 + 16*a /       
- ------------------- + -------------------------------
            2/    pi\              4        2         6
  -1 + a*cos |9 - --|   -1 - 1792*a  + 112*a  + 4096*a 
             \    2 /

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \cos^{2}{\left(9 - \frac{\pi}{2} \right)} - 1}

                                  a      
                           1 - -------   
                                  2      
   sec(4*acot(4*a))            sec (9)   
--------------------- - -----------------
   /              pi\             a      
sec|4*acot(4*a) - --|   -1 + ------------
   \              2 /           2/    pi\
                             sec |9 - --|
                                 \    2 /

- \frac{- \frac{a}{\sec^{2}{\left(9 \right)}} + 1}{\frac{a}{\sec^{2}{\left(9 - \frac{\pi}{2} \right)}} - 1} + \frac{\sec{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\sec{\left(4 \operatorname{acot}{\left(4 a \right)} - \frac{\pi}{2} \right)}}

                            2    
sin(4*acot(4*a))   1 - a*cos (9) 
---------------- - --------------
cos(4*acot(4*a))             2   
                   -1 + a*sin (9)

\frac{\sin{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\cos{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

               3       /          2   \
  -16*a + 256*a      2*\-1 + a*cos (9)/
------------------ - ------------------
        2        4   2 - a + a*cos(18) 
1 - 96*a  + 256*a

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{2 \left(a \cos^{2}{\left(9 \right)} - 1\right)}{- a + a \cos{\left(18 \right)} + 2}

                                  a      
                        1 - -------------
   /pi              \          2/     pi\
csc|-- - 4*acot(4*a)|       csc |-9 + --|
   \2               /           \     2 /
--------------------- - -----------------
   csc(4*acot(4*a))                a     
                           -1 + -------  
                                   2     
                                csc (9)

\frac{\csc{\left(- 4 \operatorname{acot}{\left(4 a \right)} + \frac{\pi}{2} \right)}}{\csc{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{- \frac{a}{\csc^{2}{\left(-9 + \frac{\pi}{2} \right)}} + 1}{\frac{a}{\csc^{2}{\left(9 \right)}} - 1}

            a                           
     1 - -------                        
            2              /         2\ 
         sec (9)      16*a*\-1 + 16*a / 
- ----------------- + ------------------
            a                 2        4
  -1 + ------------   1 - 96*a  + 256*a 
          2/    pi\                     
       sec |9 - --|                     
           \    2 /

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{- \frac{a}{\sec^{2}{\left(9 \right)}} + 1}{\frac{a}{\sec^{2}{\left(9 - \frac{\pi}{2} \right)}} - 1}

                                       a      
                        -2 + a + -------------
   /pi              \               /      pi\
csc|-- - 4*acot(4*a)|            csc|-18 + --|
   \2               /               \      2 /
--------------------- - ----------------------
   csc(4*acot(4*a))                   a       
                        2 - a + ------------- 
                                   /      pi\ 
                                csc|-18 + --| 
                                   \      2 /

\frac{\csc{\left(- 4 \operatorname{acot}{\left(4 a \right)} + \frac{\pi}{2} \right)}}{\csc{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{\frac{a}{\csc{\left(-18 + \frac{\pi}{2} \right)}} + a - 2}{- a + \frac{a}{\csc{\left(-18 + \frac{\pi}{2} \right)}} + 2}

                                         2
                         /        2     \ 
                       a*\-1 + cot (9/2)/ 
                   1 - -------------------
                                        2 
                         /       2     \  
       1                 \1 + cot (9/2)/  
---------------- - -----------------------
cot(4*acot(4*a))                 2        
                          4*a*cot (9/2)   
                    -1 + ---------------- 
                                        2 
                         /       2     \  
                         \1 + cot (9/2)/

- \frac{- \frac{a \left(-1 + \cot^{2}{\left(\frac{9}{2} \right)}\right)^{2}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} + 1}{\frac{4 a \cot^{2}{\left(\frac{9}{2} \right)}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} - 1} + \frac{1}{\cot{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}

               3                       
  -16*a + 256*a      -2 + a + a*cos(18)
------------------ - ------------------
        2        4   2 - a + a*cos(18) 
1 - 96*a  + 256*a

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{a \cos{\left(18 \right)} + a - 2}{- a + a \cos{\left(18 \right)} + 2}

                                          2
                           /       2     \ 
                         a*\1 - tan (9/2)/ 
                     1 - ------------------
                                         2 
               3          /       2     \  
  -16*a + 256*a           \1 + tan (9/2)/  
------------------ - ----------------------
        2        4                2        
1 - 96*a  + 256*a          4*a*tan (9/2)   
                     -1 + ---------------- 
                                         2 
                          /       2     \  
                          \1 + tan (9/2)/

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{- \frac{a \left(1 - \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} + 1}{\frac{4 a \tan^{2}{\left(\frac{9}{2} \right)}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} - 1}

            a                                        
     1 - -------                              2      
            2                     /         2\       
         sec (9)             16*a*\-1 + 16*a /       
- ----------------- + -------------------------------
            a                    4        2         6
  -1 + ------------   -1 - 1792*a  + 112*a  + 4096*a 
          2/    pi\                                  
       sec |9 - --|                                  
           \    2 /

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{- \frac{a}{\sec^{2}{\left(9 \right)}} + 1}{\frac{a}{\sec^{2}{\left(9 - \frac{\pi}{2} \right)}} - 1}

           2            2             
  1 - a*cos (9)    2*sin (4*acot(4*a))
- -------------- + -------------------
            2        sin(8*acot(4*a)) 
  -1 + a*sin (9)

\frac{2 \sin^{2}{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\sin{\left(8 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

           2/    pi\                     
  1 - a*sin |9 + --|        /         2\ 
            \    2 /   16*a*\-1 + 16*a / 
- ------------------ + ------------------
              2                2        4
    -1 + a*sin (9)     1 - 96*a  + 256*a

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{- a \sin^{2}{\left(\frac{\pi}{2} + 9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

                               a      
                        1 - -------   
               3               2      
  -16*a + 256*a             sec (9)   
------------------ - -----------------
        2        4             a      
1 - 96*a  + 256*a    -1 + ------------
                             2/    pi\
                          sec |9 - --|
                              \    2 /

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{- \frac{a}{\sec^{2}{\left(9 \right)}} + 1}{\frac{a}{\sec^{2}{\left(9 - \frac{\pi}{2} \right)}} - 1}

                       2                     
        /       2     \                      
      a*\1 - tan (9/2)/                      
  1 - ------------------                     
                      2                      
       /       2     \          /         2\ 
       \1 + tan (9/2)/     16*a*\-1 + 16*a / 
- ---------------------- + ------------------
               2                   2        4
        4*a*tan (9/2)      1 - 96*a  + 256*a 
  -1 + ----------------                      
                      2                      
       /       2     \                       
       \1 + tan (9/2)/

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{- \frac{a \left(1 - \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} + 1}{\frac{4 a \tan^{2}{\left(\frac{9}{2} \right)}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} - 1}

   /              pi\                      
cos|4*acot(4*a) - --|               2      
   \              2 /      1 - a*cos (9)   
--------------------- - -------------------
   cos(4*acot(4*a))               2/    pi\
                        -1 + a*cos |9 - --|
                                   \    2 /

- \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \cos^{2}{\left(9 - \frac{\pi}{2} \right)} - 1} + \frac{\cos{\left(4 \operatorname{acot}{\left(4 a \right)} - \frac{\pi}{2} \right)}}{\cos{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}

                                           2      
           2                   /         2\       
  1 - a*cos (9)           16*a*\-1 + 16*a /       
- -------------- + -------------------------------
            2                 4        2         6
  -1 + a*sin (9)   -1 - 1792*a  + 112*a  + 4096*a

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

           2/    pi\                      
  1 - a*sin |9 + --|        2             
            \    2 /   2*sin (4*acot(4*a))
- ------------------ + -------------------
              2          sin(8*acot(4*a)) 
    -1 + a*sin (9)

\frac{2 \sin^{2}{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\sin{\left(8 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{- a \sin^{2}{\left(\frac{\pi}{2} + 9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1}

            a                                        
  1 - -------------                                  
         2/     pi\                           2      
      csc |-9 + --|               /         2\       
          \     2 /          16*a*\-1 + 16*a /       
- ----------------- + -------------------------------
             a                   4        2         6
     -1 + -------     -1 - 1792*a  + 112*a  + 4096*a 
             2                                       
          csc (9)

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{- \frac{a}{\csc^{2}{\left(-9 + \frac{\pi}{2} \right)}} + 1}{\frac{a}{\csc^{2}{\left(9 \right)}} - 1}

               3                 2      
  -16*a + 256*a         1 - a*cos (9)   
------------------ - -------------------
        2        4             2/    pi\
1 - 96*a  + 256*a    -1 + a*cos |9 - --|
                                \    2 /

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \cos^{2}{\left(9 - \frac{\pi}{2} \right)} - 1}

                            /         2\ 
  -2 + a + a*cos(18)   16*a*\-1 + 16*a / 
- ------------------ + ------------------
  2 - a + a*cos(18)            2        4
                       1 - 96*a  + 256*a

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{a \cos{\left(18 \right)} + a - 2}{- a + a \cos{\left(18 \right)} + 2}

                /     pi\                      
  -2 + a + a*sin|18 + --|        2             
                \     2 /   2*sin (4*acot(4*a))
- ----------------------- + -------------------
                /     pi\     sin(8*acot(4*a)) 
   2 - a + a*sin|18 + --|                      
                \     2 /

\frac{2 \sin^{2}{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\sin{\left(8 \operatorname{acot}{\left(4 a \right)} \right)}} - \frac{a \sin{\left(\frac{\pi}{2} + 18 \right)} + a - 2}{- a + a \sin{\left(\frac{\pi}{2} + 18 \right)} + 2}

                                                      2      
                                    /        2       \       
                                    |     sec (9/2)  |       
                                  a*|1 - ------------|       
                                    |       2/9   pi\|       
                                    |    sec |- - --||       
                                    \        \2   2 //       
                              1 - ---------------------      
                                                     2       
                                   /        2       \        
                                   |     sec (9/2)  |        
                                   |1 + ------------|        
                                   |       2/9   pi\|        
                                   |    sec |- - --||        
   sec(4*acot(4*a))                \        \2   2 //        
--------------------- - -------------------------------------
   /              pi\                        2               
sec|4*acot(4*a) - --|                 4*a*sec (9/2)          
   \              2 /   -1 + --------------------------------
                                               2             
                             /        2       \              
                             |     sec (9/2)  |     2/9   pi\
                             |1 + ------------| *sec |- - --|
                             |       2/9   pi\|      \2   2 /
                             |    sec |- - --||              
                             \        \2   2 //

- \frac{- \frac{a \left(- \frac{\sec^{2}{\left(\frac{9}{2} \right)}}{\sec^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\left(1 + \frac{\sec^{2}{\left(\frac{9}{2} \right)}}{\sec^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}\right)^{2}} + 1}{\frac{4 a \sec^{2}{\left(\frac{9}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{9}{2} \right)}}{\sec^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}\right)^{2} \sec^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}} - 1} + \frac{\sec{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\sec{\left(4 \operatorname{acot}{\left(4 a \right)} - \frac{\pi}{2} \right)}}

                       2                   
        /       2     \                    
      a*\1 - tan (9/2)/                    
  1 - ------------------                   
                      2                    
       /       2     \                     
       \1 + tan (9/2)/                     
- ---------------------- + tan(4*acot(4*a))
               2                           
        4*a*tan (9/2)                      
  -1 + ----------------                    
                      2                    
       /       2     \                     
       \1 + tan (9/2)/

- \frac{- \frac{a \left(1 - \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} + 1}{\frac{4 a \tan^{2}{\left(\frac{9}{2} \right)}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} - 1} + \tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}

                                    a   
                        -2 + a + -------
   sec(4*acot(4*a))              sec(18)
--------------------- - ----------------
   /              pi\              a    
sec|4*acot(4*a) - --|   2 - a + ------- 
   \              2 /           sec(18)

\frac{\sec{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}{\sec{\left(4 \operatorname{acot}{\left(4 a \right)} - \frac{\pi}{2} \right)}} - \frac{\frac{a}{\sec{\left(18 \right)}} + a - 2}{- a + \frac{a}{\sec{\left(18 \right)}} + 2}

                        2                                  
        /        2     \                                   
      a*\-1 + cot (9/2)/                                   
  1 - -------------------                                  
                       2                            2      
        /       2     \                 /         2\       
        \1 + cot (9/2)/            16*a*\-1 + 16*a /       
- ----------------------- + -------------------------------
                2                      4        2         6
         4*a*cot (9/2)      -1 - 1792*a  + 112*a  + 4096*a 
   -1 + ----------------                                   
                       2                                   
        /       2     \                                    
        \1 + cot (9/2)/

\frac{16 a \left(16 a^{2} - 1\right)^{2}}{4096 a^{6} - 1792 a^{4} + 112 a^{2} - 1} - \frac{- \frac{a \left(-1 + \cot^{2}{\left(\frac{9}{2} \right)}\right)^{2}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} + 1}{\frac{4 a \cot^{2}{\left(\frac{9}{2} \right)}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} - 1}

  -2 + a + a*cos(18)                   
- ------------------ + tan(4*acot(4*a))
  2 - a + a*cos(18)

\tan{\left(4 \operatorname{acot}{\left(4 a \right)} \right)} - \frac{a \cos{\left(18 \right)} + a - 2}{- a + a \cos{\left(18 \right)} + 2}

            a                           
  1 - -------------                     
         2/     pi\                     
      csc |-9 + --|        /         2\ 
          \     2 /   16*a*\-1 + 16*a / 
- ----------------- + ------------------
             a                2        4
     -1 + -------     1 - 96*a  + 256*a 
             2                          
          csc (9)

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{- \frac{a}{\csc^{2}{\left(-9 + \frac{\pi}{2} \right)}} + 1}{\frac{a}{\csc^{2}{\left(9 \right)}} - 1}

    /          2   \        /         2\ 
  2*\-1 + a*cos (9)/   16*a*\-1 + 16*a / 
- ------------------ + ------------------
  2 - a + a*cos(18)            2        4
                       1 - 96*a  + 256*a

\frac{16 a \left(16 a^{2} - 1\right)}{256 a^{4} - 96 a^{2} + 1} - \frac{2 \left(a \cos^{2}{\left(9 \right)} - 1\right)}{- a + a \cos{\left(18 \right)} + 2}

                                           2
                           /        2     \ 
                         a*\-1 + cot (9/2)/ 
                     1 - -------------------
                                          2 
               3           /       2     \  
  -16*a + 256*a            \1 + cot (9/2)/  
------------------ - -----------------------
        2        4                 2        
1 - 96*a  + 256*a           4*a*cot (9/2)   
                      -1 + ---------------- 
                                          2 
                           /       2     \  
                           \1 + cot (9/2)/

\frac{256 a^{3} - 16 a}{256 a^{4} - 96 a^{2} + 1} - \frac{- \frac{a \left(-1 + \cot^{2}{\left(\frac{9}{2} \right)}\right)^{2}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} + 1}{\frac{4 a \cot^{2}{\left(\frac{9}{2} \right)}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} - 1}

                                             2    
                              /        1    \     
                            a*|1 - ---------|     
                              |       2     |     
                              \    cot (9/2)/     
                        1 - ------------------    
                                            2     
                             /        1    \      
                             |1 + ---------|      
                             |       2     |      
       1                     \    cot (9/2)/      
---------------- - -------------------------------
cot(4*acot(4*a))                   4*a            
                   -1 + --------------------------
                                       2          
                        /        1    \     2     
                        |1 + ---------| *cot (9/2)
                        |       2     |           
                        \    cot (9/2)/

- \frac{- \frac{a \left(1 - \frac{1}{\cot^{2}{\left(\frac{9}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{9}{2} \right)}}\right)^{2}} + 1}{\frac{4 a}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{9}{2} \right)}}\right)^{2} \cot^{2}{\left(\frac{9}{2} \right)}} - 1} + \frac{1}{\cot{\left(4 \operatorname{acot}{\left(4 a \right)} \right)}}

1/cot(4*acot(4*a)) - (1 - a*(1 - 1/cot(9/2)^2)^2/(1 + cot(9/2)^(-2))^2)/(-1 + 4*a/((1 + cot(9/2)^(-2))^2*cot(9/2)^2))

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