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(x^4-2*x^3+3*x^2)/(x^4-x^2+4*x-4)
2*x*(-3+4*x^2/(-1+x^2))/(-1+x^2)^2
(2*x-12)/(x-6)
(4s^2+4s-2)/((-s*(s^2+2*s+2)))+4/s
Factorizar el polinomio:
x+9*x^4
-x+x^2-3*x
-x+x^2/14
x^9+3*x^7+3*x5+x^3-x+7
Descomponer al cuadrado:
-y^4+2*y^2-2
y^4-15*y^2-1
-y^4+15*y^2-10
-y^4-14*y^2-9
Expresiones idénticas
(sin(a-pi)^ dos - cuatro *cos(tres *pi/ dos -a/ dos)^ dos)/(cos(a- cinco *pi/ dos)^ dos + cuatro *cos(pi/ dos +a/ dos)^ dos - cuatro)
( seno de (a menos número pi ) al cuadrado menos 4 multiplicar por coseno de (3 multiplicar por número pi dividir por 2 menos a dividir por 2) al cuadrado ) dividir por ( coseno de (a menos 5 multiplicar por número pi dividir por 2) al cuadrado más 4 multiplicar por coseno de ( número pi dividir por 2 más a dividir por 2) al cuadrado menos 4)
( seno de (a menos número pi ) en el grado dos menos cuatro multiplicar por coseno de (tres multiplicar por número pi dividir por dos menos a dividir por dos) en el grado dos) dividir por ( coseno de (a menos cinco multiplicar por número pi dividir por dos) en el grado dos más cuatro multiplicar por coseno de ( número pi dividir por dos más a dividir por dos) en el grado dos menos cuatro)
(sin(a-pi)2-4*cos(3*pi/2-a/2)2)/(cos(a-5*pi/2)2+4*cos(pi/2+a/2)2-4)
sina-pi2-4*cos3*pi/2-a/22/cosa-5*pi/22+4*cospi/2+a/22-4
(sin(a-pi)²-4*cos(3*pi/2-a/2)²)/(cos(a-5*pi/2)²+4*cos(pi/2+a/2)²-4)
(sin(a-pi) en el grado 2-4*cos(3*pi/2-a/2) en el grado 2)/(cos(a-5*pi/2) en el grado 2+4*cos(pi/2+a/2) en el grado 2-4)
(sin(a-pi)^2-4cos(3pi/2-a/2)^2)/(cos(a-5pi/2)^2+4cos(pi/2+a/2)^2-4)
(sin(a-pi)2-4cos(3pi/2-a/2)2)/(cos(a-5pi/2)2+4cos(pi/2+a/2)2-4)
sina-pi2-4cos3pi/2-a/22/cosa-5pi/22+4cospi/2+a/22-4
sina-pi^2-4cos3pi/2-a/2^2/cosa-5pi/2^2+4cospi/2+a/2^2-4
(sin(a-pi)^2-4*cos(3*pi dividir por 2-a dividir por 2)^2) dividir por (cos(a-5*pi dividir por 2)^2+4*cos(pi dividir por 2+a dividir por 2)^2-4)
Expresiones semejantes
(sin(a-pi)^2+4*cos(3*pi/2-a/2)^2)/(cos(a-5*pi/2)^2+4*cos(pi/2+a/2)^2-4)
(sin(a-pi)^2-4*cos(3*pi/2-a/2)^2)/(cos(a-5*pi/2)^2+4*cos(pi/2+a/2)^2+4)
(sin(a-pi)^2-4*cos(3*pi/2+a/2)^2)/(cos(a-5*pi/2)^2+4*cos(pi/2+a/2)^2-4)
(sin(a+pi)^2-4*cos(3*pi/2-a/2)^2)/(cos(a-5*pi/2)^2+4*cos(pi/2+a/2)^2-4)
(sin(a-pi)^2-4*cos(3*pi/2-a/2)^2)/(cos(a-5*pi/2)^2-4*cos(pi/2+a/2)^2-4)
(sin(a-pi)^2-4*cos(3*pi/2-a/2)^2)/(cos(a+5*pi/2)^2+4*cos(pi/2+a/2)^2-4)
(sin(a-pi)^2-4*cos(3*pi/2-a/2)^2)/(cos(a-5*pi/2)^2+4*cos(pi/2-a/2)^2-4)
Expresiones con funciones
Seno sin
sin(2*a-2*sin(a))/(cos(a)-1)
sin(180*pi/(360-a))^2+sin(270*pi/(360-a))^2
sin(180/(2^(n+1)))/sin(180/(2^n))

Simplificación de expresiones/ Descomposición en fracciones simples/ (sin(a-pi)^2-4*cos(3*pi/2-a/2)^2)/(cos(a-5*pi/2)^2+4*cos(pi/2+a/2)^2-4)

¿Cómo vas a descomponer esta (sin(a-pi)^2-4cos(3pi/2-a/2)^2)/(cos(a-5pi/2)^2+4cos(pi/2+a/2)^2-4) expresión en fracciones?

Solución

Ha introducido [src]

     2                2/3*pi   a\  
  sin (a - pi) - 4*cos |---- - -|  
                       \ 2     2/  
-----------------------------------
   2/    5*pi\        2/pi   a\    
cos |a - ----| + 4*cos |-- + -| - 4
    \     2  /         \2    2/

\frac{\sin^{2}{\left(a - \pi \right)} - 4 \cos^{2}{\left(- \frac{a}{2} + \frac{3 \pi}{2} \right)}}{\left(\cos^{2}{\left(a - \frac{5 \pi}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}\right) - 4}

(sin(a - pi)^2 - 4*cos((3*pi)/2 - a/2)^2)/(cos(a - 5*pi/2)^2 + 4*cos(pi/2 + a/2)^2 - 4)

Simplificación general [src]

3 - 4*cos(a) + cos(2*a)
-----------------------
3 + 4*cos(a) + cos(2*a)

\frac{- 4 \cos{\left(a \right)} + \cos{\left(2 a \right)} + 3}{4 \cos{\left(a \right)} + \cos{\left(2 a \right)} + 3}

(3 - 4*cos(a) + cos(2*a))/(3 + 4*cos(a) + cos(2*a))

Respuesta numérica [src]

(sin(a - pi)^2 - 4.0*cos((3*pi)/2 - a/2)^2)/(-4.0 + cos(a - 5*pi/2)^2 + 4.0*cos(pi/2 + a/2)^2)

(sin(a - pi)^2 - 4.0*cos((3*pi)/2 - a/2)^2)/(-4.0 + cos(a - 5*pi/2)^2 + 4.0*cos(pi/2 + a/2)^2)

Denominador racional [src]

           2           2/a\         
        sin (a) - 4*sin |-|         
                        \2/         
------------------------------------
        2/    5*pi\        2/pi   a\
-4 + cos |a - ----| + 4*cos |-- + -|
         \     2  /         \2    2/

\frac{- 4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{5 \pi}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} - 4}

(sin(a)^2 - 4*sin(a/2)^2)/(-4 + cos(a - 5*pi/2)^2 + 4*cos(pi/2 + a/2)^2)

Potencias [src]

                                      2                                  
     /   /a   3*pi\      /  a   3*pi\\                                   
     | I*|- - ----|    I*|- - + ----||                                 2 
     |   \2    2  /      \  2    2  /|    /   I*(pi - a)    I*(a - pi)\  
     |e               e              |    \- e           + e          /  
 - 4*|------------- + ---------------|  - ------------------------------ 
     \      2                2       /                  4                
-------------------------------------------------------------------------
                                     2                                  2
     /   /    5*pi\      /     5*pi\\      /   /pi   a\      /  pi   a\\ 
     | I*|a - ----|    I*|-a + ----||      | I*|-- + -|    I*|- -- - -|| 
     |   \     2  /      \      2  /|      |   \2    2/      \  2    2/| 
     |e               e             |      |e             e            | 
-4 + |------------- + --------------|  + 4*|----------- + -------------| 
     \      2               2       /      \     2              2      /

\frac{- \frac{\left(- e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right)^{2}}{4} - 4 \left(\frac{e^{i \left(- \frac{a}{2} + \frac{3 \pi}{2}\right)}}{2} + \frac{e^{i \left(\frac{a}{2} - \frac{3 \pi}{2}\right)}}{2}\right)^{2}}{\left(\frac{e^{i \left(- a + \frac{5 \pi}{2}\right)}}{2} + \frac{e^{i \left(a - \frac{5 \pi}{2}\right)}}{2}\right)^{2} + 4 \left(\frac{e^{i \left(- \frac{a}{2} - \frac{\pi}{2}\right)}}{2} + \frac{e^{i \left(\frac{a}{2} + \frac{\pi}{2}\right)}}{2}\right)^{2} - 4}

     2           2/a\   
  sin (a) - 4*sin |-|   
                  \2/   
------------------------
        2           2/a\
-4 + sin (a) + 4*sin |-|
                     \2/

\frac{- 4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}}{4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)} - 4}

(sin(a)^2 - 4*sin(a/2)^2)/(-4 + sin(a)^2 + 4*sin(a/2)^2)

Combinatoria [src]

/       /a\         \ /     /a\         \
|- 2*sin|-| + sin(a)|*|2*sin|-| + sin(a)|
\       \2/         / \     \2/         /
-----------------------------------------
                 2           2/a\        
         -4 + sin (a) + 4*sin |-|        
                              \2/

\frac{\left(- 2 \sin{\left(\frac{a}{2} \right)} + \sin{\left(a \right)}\right) \left(2 \sin{\left(\frac{a}{2} \right)} + \sin{\left(a \right)}\right)}{4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)} - 4}

(-2*sin(a/2) + sin(a))*(2*sin(a/2) + sin(a))/(-4 + sin(a)^2 + 4*sin(a/2)^2)

Unión de expresiones racionales [src]

         2           2/-a + 3*pi\      
      sin (a) - 4*cos |---------|      
                      \    2    /      
---------------------------------------
        2/-5*pi + 2*a\        2/pi + a\
-4 + cos |-----------| + 4*cos |------|
         \     2     /         \  2   /

\frac{\sin^{2}{\left(a \right)} - 4 \cos^{2}{\left(\frac{- a + 3 \pi}{2} \right)}}{4 \cos^{2}{\left(\frac{a + \pi}{2} \right)} + \cos^{2}{\left(\frac{2 a - 5 \pi}{2} \right)} - 4}

(sin(a)^2 - 4*cos((-a + 3*pi)/2)^2)/(-4 + cos((-5*pi + 2*a)/2)^2 + 4*cos((pi + a)/2)^2)

Abrimos la expresión [src]

                                       2/a\        
           2                      4*sin |-|        
        sin (a)                         \2/        
------------------------ - ------------------------
        2           2/a\           2           2/a\
-4 + sin (a) + 4*sin |-|   -4 + sin (a) + 4*sin |-|
                     \2/                        \2/

- \frac{4 \sin^{2}{\left(\frac{a}{2} \right)}}{4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)} - 4} + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)} - 4}

sin(a)^2/(-4 + sin(a)^2 + 4*sin(a/2)^2) - 4*sin(a/2)^2/(-4 + sin(a)^2 + 4*sin(a/2)^2)

Compilar la expresión [src]

     2                2/3*pi   a\   
  sin (a - pi) - 4*cos |---- - -|   
                       \ 2     2/   
------------------------------------
        2/    5*pi\        2/pi   a\
-4 + cos |a - ----| + 4*cos |-- + -|
         \     2  /         \2    2/

\frac{\sin^{2}{\left(a - \pi \right)} - 4 \cos^{2}{\left(- \frac{a}{2} + \frac{3 \pi}{2} \right)}}{\cos^{2}{\left(a - \frac{5 \pi}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} - 4}

(sin(a - pi)^2 - 4*cos((3*pi)/2 - a/2)^2)/(-4 + cos(a - 5*pi/2)^2 + 4*cos(pi/2 + a/2)^2)

Denominador común [src]

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

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

(sin(a - pi)^2 - 4*sin(a/2)^2)/(-4 + sin(a)^2 + 4*sin(a/2)^2)

Parte trigonométrica [src]

      1             4   
-------------- - -------
   2/    3*pi\      2/a\
sec |a - ----|   csc |-|
    \     2  /       \2/
------------------------
         1         4    
 -4 + ------- + ------- 
         2         2/a\ 
      csc (a)   csc |-| 
                    \2/

\frac{\frac{1}{\sec^{2}{\left(a - \frac{3 \pi}{2} \right)}} - \frac{4}{\csc^{2}{\left(\frac{a}{2} \right)}}}{-4 + \frac{1}{\csc^{2}{\left(a \right)}} + \frac{4}{\csc^{2}{\left(\frac{a}{2} \right)}}}

            2/    pi\         2/  pi   a\         4/  pi   a\        
         cos |a - --| - 16*cos |- -- + -| + 16*cos |- -- + -|        
             \    2 /          \  2    4/          \  2    4/        
---------------------------------------------------------------------
                                                 2                   
                               /       2/a   pi\\                    
                               |    cos |- + --||                   2
                               |        \2   4 /|  /       /    pi\\ 
                               |1 - ------------| *|1 + cos|a - --|| 
                               |       2/a   pi\|  \       \    2 // 
                               |    cos |- - --||                    
           4/a\         2/a\   \        \2   4 //                    
-4 - 16*cos |-| + 16*cos |-| + --------------------------------------
            \4/          \4/                     4

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

 /       /        2/a\\          2/a\   \ 
 |     2*|-1 + cot |-||     4*cot |-|   | 
 |       \         \2//           \2/   | 
-|-2 + ---------------- + --------------| 
 |              2/a\                   2| 
 |       1 + cot |-|      /       2/a\\ | 
 |               \2/      |1 + cot |-|| | 
 \                        \        \2// / 
------------------------------------------
                             2            
           /            2/a\\             
           |    -1 + cot |-||             
           |             \2/|             
           |1 + ------------|             
           |           2/a\ |             
           |    1 + cot |-| |             
           \            \2/ /

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

                1 - cos(2*a)     /       /a\\          4/a\    8/a\                 
                ------------ - 8*|1 - cos|-|| + 256*cot |-|*sin |-|                 
                     2           \       \2//           \8/     \8/                 
------------------------------------------------------------------------------------
                                                                     2              
                                                   /       2/a   pi\\              2
                                       4           |1 - cot |- + --|| *(1 + sin(a)) 
       /       /a\\      /        2/a\\     8/a\   \        \2   4 //               
-4 + 8*|1 + cos|-|| - 16*|-1 + cot |-|| *sin |-| + ---------------------------------
       \       \2//      \         \8//      \8/                   4

\frac{- 8 \left(1 - \cos{\left(\frac{a}{2} \right)}\right) + \frac{1 - \cos{\left(2 a \right)}}{2} + 256 \sin^{8}{\left(\frac{a}{8} \right)} \cot^{4}{\left(\frac{a}{8} \right)}}{\frac{\left(1 - \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)^{2} \left(\sin{\left(a \right)} + 1\right)^{2}}{4} + 8 \left(\cos{\left(\frac{a}{2} \right)} + 1\right) - 16 \left(\cot^{2}{\left(\frac{a}{8} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{a}{8} \right)} - 4}

       1         4   
3 + -------- - ------
    sec(2*a)   sec(a)
---------------------
       1         4   
3 + -------- + ------
    sec(2*a)   sec(a)

\frac{3 + \frac{1}{\sec{\left(2 a \right)}} - \frac{4}{\sec{\left(a \right)}}}{3 + \frac{1}{\sec{\left(2 a \right)}} + \frac{4}{\sec{\left(a \right)}}}

         /    pi\      /pi      \
3 - 4*sin|a + --| + sin|-- + 2*a|
         \    2 /      \2       /
---------------------------------
         /    pi\      /pi      \
3 + 4*sin|a + --| + sin|-- + 2*a|
         \    2 /      \2       /

\frac{- 4 \sin{\left(a + \frac{\pi}{2} \right)} + \sin{\left(2 a + \frac{\pi}{2} \right)} + 3}{4 \sin{\left(a + \frac{\pi}{2} \right)} + \sin{\left(2 a + \frac{\pi}{2} \right)} + 3}

 /       /       2/a\\          2/a\   \ 
 |     2*|1 - tan |-||     4*tan |-|   | 
 |       \        \2//           \2/   | 
-|-2 + --------------- + --------------| 
 |              2/a\                  2| 
 |       1 + tan |-|     /       2/a\\ | 
 |               \2/     |1 + tan |-|| | 
 \                       \        \2// / 
-----------------------------------------
                             2           
            /           2/a\\            
            |    1 - tan |-||            
            |            \2/|            
            |1 + -----------|            
            |           2/a\|            
            |    1 + tan |-||            
            \            \2//

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

                          2                     
        /       2/pi   a\\           2/a\       
      4*|1 - tan |-- + -||      4*cot |-|       
        \        \4    4//            \2/       
    - --------------------- + --------------    
                         2                 2    
       /       2/pi   a\\     /       2/a\\     
       |1 + tan |-- + -||     |1 + cot |-||     
       \        \4    4//     \        \2//     
------------------------------------------------
                       2                       2
     /       2/a   pi\\      /       2/pi   a\\ 
     |1 - cot |- + --||    4*|1 - tan |-- + -|| 
     \        \2   4 //      \        \4    4// 
-4 + ------------------- + ---------------------
                       2                      2 
     /       2/a   pi\\     /       2/pi   a\\  
     |1 + cot |- + --||     |1 + tan |-- + -||  
     \        \2   4 //     \        \4    4//

\frac{- \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{\pi}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{4} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}}{\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{\pi}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{4} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{\left(1 - \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} - 4}

                           2/a\            2/a\              4/a\                  
                     64*tan |-|       4*tan |-|       256*tan |-|                  
                            \8/             \2/               \8/                  
                 - -------------- + -------------- + --------------                
                                2                2                4                
                   /       2/a\\    /       2/a\\    /       2/a\\                 
                   |1 + tan |-||    |1 + tan |-||    |1 + tan |-||                 
                   \        \8//    \        \2//    \        \8//                 
-----------------------------------------------------------------------------------
                                                                                  2
                                                                 /           /a\ \ 
                                                               2 |      2*tan|-| | 
                                             /         1      \  |           \2/ | 
                     4                   2   |1 - ------------| *|1 + -----------| 
        /       2/a\\       /       2/a\\    |       2/a   pi\|  |           2/a\| 
     16*|1 - tan |-||    16*|1 - tan |-||    |    tan |- + --||  |    1 + tan |-|| 
        \        \8//       \        \8//    \        \2   4 //  \            \2// 
-4 - ----------------- + ----------------- + --------------------------------------
                    4                   2                      4                   
       /       2/a\\       /       2/a\\                                           
       |1 + tan |-||       |1 + tan |-||                                           
       \        \8//       \        \8//

\frac{\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - \frac{64 \tan^{2}{\left(\frac{a}{8} \right)}}{\left(\tan^{2}{\left(\frac{a}{8} \right)} + 1\right)^{2}} + \frac{256 \tan^{4}{\left(\frac{a}{8} \right)}}{\left(\tan^{2}{\left(\frac{a}{8} \right)} + 1\right)^{4}}}{\frac{\left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right)^{2} \left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)^{2}}{4} - \frac{16 \left(1 - \tan^{2}{\left(\frac{a}{8} \right)}\right)^{4}}{\left(\tan^{2}{\left(\frac{a}{8} \right)} + 1\right)^{4}} + \frac{16 \left(1 - \tan^{2}{\left(\frac{a}{8} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{8} \right)} + 1\right)^{2}} - 4}

     2           2/a\   
  sin (a) - 4*sin |-|   
                  \2/   
------------------------
        2           2/a\
-4 + sin (a) + 4*sin |-|
                     \2/

\frac{- 4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}}{4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)} - 4}

                      2                         
    /       2/pi   a\\                          
  4*|1 - tan |-- + -||                          
    \        \4    4//              4           
- --------------------- + ----------------------
                     2                 2        
   /       2/pi   a\\     /       1   \     2/a\
   |1 + tan |-- + -||     |1 + -------| *tan |-|
   \        \4    4//     |       2/a\|      \2/
                          |    tan |-||         
                          \        \2//         
------------------------------------------------
                       2                        
     /         1      \                         
     |1 - ------------|                        2
     |       2/a   pi\|      /       2/pi   a\\ 
     |    tan |- + --||    4*|1 - tan |-- + -|| 
     \        \2   4 //      \        \4    4// 
-4 + ------------------- + ---------------------
                       2                      2 
     /         1      \     /       2/pi   a\\  
     |1 + ------------|     |1 + tan |-- + -||  
     |       2/a   pi\|     \        \4    4//  
     |    tan |- + --||                         
     \        \2   4 //

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

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

\frac{\sin^{2}{\left(a \right)} - 4 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{4 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} + \cos^{2}{\left(a - \frac{\pi}{2} \right)} - 4}

3 - 4*cos(a) + cos(2*a)
-----------------------
3 + 4*cos(a) + cos(2*a)

\frac{- 4 \cos{\left(a \right)} + \cos{\left(2 a \right)} + 3}{4 \cos{\left(a \right)} + \cos{\left(2 a \right)} + 3}

          1              4     
3 + ------------- - -----------
       /pi      \      /pi    \
    csc|-- - 2*a|   csc|-- - a|
       \2       /      \2     /
-------------------------------
          1              4     
3 + ------------- + -----------
       /pi      \      /pi    \
    csc|-- - 2*a|   csc|-- - a|
       \2       /      \2     /

\frac{3 - \frac{4}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}}{3 + \frac{4}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}}

                            2/a\            2/a\              4/a\                   
                      64*cot |-|       4*cot |-|       256*cot |-|                   
                             \8/             \2/               \8/                   
                  - -------------- + -------------- + --------------                 
                                 2                2                4                 
                    /       2/a\\    /       2/a\\    /       2/a\\                  
                    |1 + cot |-||    |1 + cot |-||    |1 + cot |-||                  
                    \        \8//    \        \2//    \        \8//                  
-------------------------------------------------------------------------------------
                                                                                    2
                                                                   /           /a\ \ 
                                                                 2 |      2*cot|-| | 
                                               /       2/a   pi\\  |           \2/ | 
                      4                    2   |1 - cot |- + --|| *|1 + -----------| 
        /        2/a\\       /        2/a\\    \        \2   4 //  |           2/a\| 
     16*|-1 + cot |-||    16*|-1 + cot |-||                        |    1 + cot |-|| 
        \         \8//       \         \8//                        \            \2// 
-4 - ------------------ + ------------------ + --------------------------------------
                    4                    2                       4                   
       /       2/a\\        /       2/a\\                                            
       |1 + cot |-||        |1 + cot |-||                                            
       \        \8//        \        \8//

\frac{\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - \frac{64 \cot^{2}{\left(\frac{a}{8} \right)}}{\left(\cot^{2}{\left(\frac{a}{8} \right)} + 1\right)^{2}} + \frac{256 \cot^{4}{\left(\frac{a}{8} \right)}}{\left(\cot^{2}{\left(\frac{a}{8} \right)} + 1\right)^{4}}}{\frac{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right)^{2} \left(1 - \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)^{2}}{4} - \frac{16 \left(\cot^{2}{\left(\frac{a}{8} \right)} - 1\right)^{4}}{\left(\cot^{2}{\left(\frac{a}{8} \right)} + 1\right)^{4}} + \frac{16 \left(\cot^{2}{\left(\frac{a}{8} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{8} \right)} + 1\right)^{2}} - 4}

   2            2/a\         4/a\
sin (a) - 16*sin |-| + 16*sin |-|
                 \4/          \4/
---------------------------------
             2           2/a\    
     -4 + sin (a) + 4*sin |-|    
                          \2/

\frac{16 \sin^{4}{\left(\frac{a}{4} \right)} - 16 \sin^{2}{\left(\frac{a}{4} \right)} + \sin^{2}{\left(a \right)}}{4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)} - 4}

                1 - cos(2*a)     /       /a\\          8/a\    4/a\                
                ------------ - 8*|1 - cos|-|| + 256*cos |-|*tan |-|                
                     2           \       \2//           \8/     \8/                
-----------------------------------------------------------------------------------
                                                                    2              
                                                  /         1      \              2
                                                  |1 - ------------| *(1 + sin(a)) 
                                                  |       2/a   pi\|               
                                      4           |    tan |- + --||               
       /       /a\\      /       2/a\\     8/a\   \        \2   4 //               
-4 + 8*|1 + cos|-|| - 16*|1 - tan |-|| *cos |-| + ---------------------------------
       \       \2//      \        \8//      \8/                   4

\frac{- 8 \left(1 - \cos{\left(\frac{a}{2} \right)}\right) + \frac{1 - \cos{\left(2 a \right)}}{2} + 256 \cos^{8}{\left(\frac{a}{8} \right)} \tan^{4}{\left(\frac{a}{8} \right)}}{- 16 \left(1 - \tan^{2}{\left(\frac{a}{8} \right)}\right)^{4} \cos^{8}{\left(\frac{a}{8} \right)} + \frac{\left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)^{2} \left(\sin{\left(a \right)} + 1\right)^{2}}{4} + 8 \left(\cos{\left(\frac{a}{2} \right)} + 1\right) - 4}

                  2            2/a\         4/a\                
               sin (a) - 16*sin |-| + 16*sin |-|                
                                \4/          \4/                
----------------------------------------------------------------
                                                 2              
                               /       2/a   pi\\              2
                               |1 - cot |- + --|| *(1 + sin(a)) 
           4/a\         2/a\   \        \2   4 //               
-4 - 16*cos |-| + 16*cos |-| + ---------------------------------
            \4/          \4/                   4

\frac{16 \sin^{4}{\left(\frac{a}{4} \right)} - 16 \sin^{2}{\left(\frac{a}{4} \right)} + \sin^{2}{\left(a \right)}}{\frac{\left(1 - \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)^{2} \left(\sin{\left(a \right)} + 1\right)^{2}}{4} - 16 \cos^{4}{\left(\frac{a}{4} \right)} + 16 \cos^{2}{\left(\frac{a}{4} \right)} - 4}

        1           4           
     ------- - ------------     
        2         2/pi   a\     
     csc (a)   sec |-- - -|     
                   \2    2/     
--------------------------------
          1              4      
-4 + ------------ + ------------
        2/pi    \      2/pi   a\
     sec |-- - a|   sec |-- - -|
         \2     /       \2    2/

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

                       2                          
    /        2/pi   a\\                           
  4*|-1 + cot |-- + -||                           
    \         \4    4//              4            
- ---------------------- + ---------------------- 
                     2                  2         
   /       2/pi   a\\      /       1   \     2/a\ 
   |1 + cot |-- + -||      |1 + -------| *cot |-| 
   \        \4    4//      |       2/a\|      \2/ 
                           |    cot |-||          
                           \        \2//          
--------------------------------------------------
                        2                         
     /          1      \                          
     |-1 + ------------|                         2
     |        2/a   pi\|      /        2/pi   a\\ 
     |     cot |- + --||    4*|-1 + cot |-- + -|| 
     \         \2   4 //      \         \4    4// 
-4 + -------------------- + ----------------------
                       2                       2  
     /         1      \      /       2/pi   a\\   
     |1 + ------------|      |1 + cot |-- + -||   
     |       2/a   pi\|      \        \4    4//   
     |    cot |- + --||                           
     \        \2   4 //

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

                        2            2/a\         4/a\                      
                     sin (a) - 16*sin |-| + 16*sin |-|                      
                                      \4/          \4/                      
----------------------------------------------------------------------------
                                                             2              
                                         /          2       \               
                                         |       cos (a)    |              2
                                         |1 - --------------| *(1 + sin(a)) 
                                         |         4/a   pi\|               
                                         |    4*sin |- + --||               
           4/pi   a\         2/pi   a\   \          \2   4 //               
-4 - 16*sin |-- + -| + 16*sin |-- + -| + -----------------------------------
            \2    4/          \2    4/                    4

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

                     /        2/a\\
            2      4*|-1 + cot |-||
    -1 + cot (a)     \         \2//
3 + ------------ - ----------------
           2                2/a\   
    1 + cot (a)      1 + cot |-|   
                             \2/   
-----------------------------------
                     /        2/a\\
            2      4*|-1 + cot |-||
    -1 + cot (a)     \         \2//
3 + ------------ + ----------------
           2                2/a\   
    1 + cot (a)      1 + cot |-|   
                             \2/

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

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

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

 /        2              \ 
-\-2 + sin (a) + 2*cos(a)/ 
---------------------------
                   2       
       (1 + cos(a))

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

              1               16               16              
         ------------ - -------------- + --------------        
            2/    pi\      2/  pi   a\      4/  pi   a\        
         sec |a - --|   sec |- -- + -|   sec |- -- + -|        
             \    2 /       \  2    4/       \  2    4/        
---------------------------------------------------------------
                                                              2
                                            /       2/a   pi\\ 
                                          2 |    sec |- - --|| 
                         /         1     \  |        \2   4 /| 
                         |1 + -----------| *|1 - ------------| 
                         |       /    pi\|  |       2/a   pi\| 
                         |    sec|a - --||  |    sec |- + --|| 
        16        16     \       \    2 //  \        \2   4 // 
-4 - ------- + ------- + --------------------------------------
        4/a\      2/a\                     4                   
     sec |-|   sec |-|                                         
         \4/       \4/

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

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

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

                    /       2/a\\
           2      4*|1 - tan |-||
    1 - tan (a)     \        \2//
3 + ----------- - ---------------
           2               2/a\  
    1 + tan (a)     1 + tan |-|  
                            \2/  
---------------------------------
                    /       2/a\\
           2      4*|1 - tan |-||
    1 - tan (a)     \        \2//
3 + ----------- + ---------------
           2               2/a\  
    1 + tan (a)     1 + tan |-|  
                            \2/

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

                           2                      
        /        2/pi   a\\           2/a\        
      4*|-1 + cot |-- + -||      4*tan |-|        
        \         \4    4//            \2/        
    - ---------------------- + --------------     
                         2                  2     
       /       2/pi   a\\      /       2/a\\      
       |1 + cot |-- + -||      |1 + tan |-||      
       \        \4    4//      \        \2//      
--------------------------------------------------
                        2                        2
     /        2/a   pi\\      /        2/pi   a\\ 
     |-1 + tan |- + --||    4*|-1 + cot |-- + -|| 
     \         \2   4 //      \         \4    4// 
-4 + -------------------- + ----------------------
                       2                       2  
     /       2/a   pi\\      /       2/pi   a\\   
     |1 + tan |- + --||      |1 + cot |-- + -||   
     \        \2   4 //      \        \4    4//

\frac{- \frac{4 \left(\cot^{2}{\left(\frac{a}{4} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{4} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}}{\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \left(\cot^{2}{\left(\frac{a}{4} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{4} + \frac{\pi}{4} \right)} + 1\right)^{2}} - 4}

   2/    3*pi\        2/a\
cos |a - ----| - 4*sin |-|
    \     2  /         \2/
--------------------------
         2           2/a\ 
 -4 + sin (a) + 4*sin |-| 
                      \2/

\frac{- 4 \sin^{2}{\left(\frac{a}{2} \right)} + \cos^{2}{\left(a - \frac{3 \pi}{2} \right)}}{4 \sin^{2}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)} - 4}

                               2           
           /a\     /       /a\\            
15 - 16*cos|-| - 8*|1 - cos|-||  + cos(2*a)
           \2/     \       \2//            
-------------------------------------------
          3 + 4*cos(a) + cos(2*a)

\frac{- 8 \left(1 - \cos{\left(\frac{a}{2} \right)}\right)^{2} - 16 \cos{\left(\frac{a}{2} \right)} + \cos{\left(2 a \right)} + 15}{4 \cos{\left(a \right)} + \cos{\left(2 a \right)} + 3}

 /          1           2   \ 
-|-2 + ------------ + ------| 
 |        2/    pi\   sec(a)| 
 |     sec |a - --|         | 
 \         \    2 /         / 
------------------------------
                    2         
        /      1   \          
        |1 + ------|          
        \    sec(a)/

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

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

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

 /        2           /    pi\\ 
-|-2 + sin (a) + 2*sin|a + --|| 
 \                    \    2 // 
--------------------------------
                        2       
       /       /    pi\\        
       |1 + sin|a + --||        
       \       \    2 //

- \frac{\sin^{2}{\left(a \right)} + 2 \sin{\left(a + \frac{\pi}{2} \right)} - 2}{\left(\sin{\left(a + \frac{\pi}{2} \right)} + 1\right)^{2}}

 /        1           2     \ 
-|-2 + ------- + -----------| 
 |        2         /pi    \| 
 |     csc (a)   csc|-- - a|| 
 \                  \2     // 
------------------------------
                       2      
      /         1     \       
      |1 + -----------|       
      |       /pi    \|       
      |    csc|-- - a||       
      \       \2     //

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

     1         4      
  ------- - -------   
     2         2/a\   
  csc (a)   csc |-|   
                \2/   
----------------------
        1         4   
-4 + ------- + -------
        2         2/a\
     csc (a)   csc |-|
                   \2/

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

(csc(a)^(-2) - 4/csc(a/2)^2)/(-4 + csc(a)^(-2) + 4/csc(a/2)^2)

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