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Simplificación de expresiones/ Descomposición en fracciones simples/ tg4a*ctg4a-((1-cos^2*9a)/(sin^2*9a-1))

¿Cómo vas a descomponer esta tg4a*ctg4a-((1-cos^2*9a)/(sin^2*9a-1)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                           2     
                    1 - cos (9)*a
tan(4*a)*cot(4*a) - -------------
                       2         
                    sin (9)*a - 1
tan⁡(4a)cot⁡(4a)−−acos⁡2(9)+1asin⁡2(9)−1\tan{\left(4 a \right)} \cot{\left(4 a \right)} - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1} 
tan(4*a)*cot(4*a) - (1 - cos(9)^2*a)/(sin(9)^2*a - 1)
Simplificación general [src] 
    -2 + a    
--------------
          2   
-1 + a*sin (9)
a−2asin⁡2(9)−1\frac{a - 2}{a \sin^{2}{\left(9 \right)} - 1} 
(-2 + a)/(-1 + a*sin(9)^2)
Respuesta numérica [src] 
cot(4*a)*tan(4*a) - (1.0 - 0.83015835412204*a)/(-1.0 + 0.16984164587796*a)
cot(4*a)*tan(4*a) - (1.0 - 0.83015835412204*a)/(-1.0 + 0.16984164587796*a)
Denominador racional [src] 
          2      /          2   \                  
-1 + a*cos (9) + \-1 + a*sin (9)/*cot(4*a)*tan(4*a)
---------------------------------------------------
                             2                     
                   -1 + a*sin (9)
acos⁡2(9)+(asin⁡2(9)−1)tan⁡(4a)cot⁡(4a)−1asin⁡2(9)−1\frac{a \cos^{2}{\left(9 \right)} + \left(a \sin^{2}{\left(9 \right)} - 1\right) \tan{\left(4 a \right)} \cot{\left(4 a \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1} 
(-1 + a*cos(9)^2 + (-1 + a*sin(9)^2)*cot(4*a)*tan(4*a))/(-1 + a*sin(9)^2)
Unión de expresiones racionales [src] 
          2      /          2   \                  
-1 + a*cos (9) + \-1 + a*sin (9)/*cot(4*a)*tan(4*a)
---------------------------------------------------
                             2                     
                   -1 + a*sin (9)
acos⁡2(9)+(asin⁡2(9)−1)tan⁡(4a)cot⁡(4a)−1asin⁡2(9)−1\frac{a \cos^{2}{\left(9 \right)} + \left(a \sin^{2}{\left(9 \right)} - 1\right) \tan{\left(4 a \right)} \cot{\left(4 a \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1} 
(-1 + a*cos(9)^2 + (-1 + a*sin(9)^2)*cot(4*a)*tan(4*a))/(-1 + a*sin(9)^2)
Potencias [src] 
          2                       
-1 + a*cos (9)                    
-------------- + cot(4*a)*tan(4*a)
          2                       
-1 + a*sin (9)
tan⁡(4a)cot⁡(4a)+acos⁡2(9)−1asin⁡2(9)−1\tan{\left(4 a \right)} \cot{\left(4 a \right)} + \frac{a \cos^{2}{\left(9 \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1} 
                       2                                    
         / -9*I    9*I\                                     
         |e       e   |                                     
   1 - a*|----- + ----|        /   4*I*a    -4*I*a\         
         \  2      2  /      I*\- e      + e      /*cot(4*a)
- ------------------------ + -------------------------------
                         2            -4*I*a    4*I*a       
         /   -9*I    9*I\            e       + e            
       a*\- e     + e   /                                   
  -1 - -------------------                                  
                4
−−a(e−9i2+e9i2)2+1−a(e9i−e−9i)24−1+i(−e4ia+e−4ia)cot⁡(4a)e4ia+e−4ia- \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 a} + e^{- 4 i a}\right) \cot{\left(4 a \right)}}{e^{4 i a} + e^{- 4 i a}} 
-(1 - a*(exp(-9*i)/2 + exp(9*i)/2)^2)/(-1 - a*(-exp(-9*i) + exp(9*i))^2/4) + i*(-exp(4*i*a) + exp(-4*i*a))*cot(4*a)/(exp(-4*i*a) + exp(4*i*a))
Combinatoria [src] 
          2                               2                     
-1 + a*cos (9) - cot(4*a)*tan(4*a) + a*sin (9)*cot(4*a)*tan(4*a)
----------------------------------------------------------------
                                   2                            
                         -1 + a*sin (9)
asin⁡2(9)tan⁡(4a)cot⁡(4a)+acos⁡2(9)−tan⁡(4a)cot⁡(4a)−1asin⁡2(9)−1\frac{a \sin^{2}{\left(9 \right)} \tan{\left(4 a \right)} \cot{\left(4 a \right)} + a \cos^{2}{\left(9 \right)} - \tan{\left(4 a \right)} \cot{\left(4 a \right)} - 1}{a \sin^{2}{\left(9 \right)} - 1} 
(-1 + a*cos(9)^2 - cot(4*a)*tan(4*a) + a*sin(9)^2*cot(4*a)*tan(4*a))/(-1 + a*sin(9)^2)
Abrimos la expresión [src] 
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                                                                                      1                                                                                                                                      4*tan (a)                                                                                                4*tan(a)                                                                                                                             559104*a*cos  (1)                                                                                                                                                            294912*a*cos  (1)                                                                                                                                                             114048*a*cos (1)                                                                                                                                                              2160*a*cos (1)                                                                                                                           24*cot (a)*tan(a)                                                                                       4*cot (a)*tan (a)                                                                                        4*cot (a)*tan(a)                                                                                       24*cot (a)*tan (a)                                                                                                                           81*a*cos (1)                                                                                                                                                               22176*a*cos (1)                                                                                                                                                              65536*a*cos  (1)                                                                                                                                                            329472*a*cos  (1)                                                                                                                                                            552960*a*cos  (1)                                                                             
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                   12                  16                  8                4              2                 6                 18                  10                  14                       3            3       2           4                  3       4            2                              3            3       2           4                  3       4            2                              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                       3            3       2           4                  3       4            2                              3            3       2           4                  3       4            2                              3            3       2           4                  3       4            2                              3            3       2           4                  3       4            2                              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   
  -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)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(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)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(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)
−114048acos⁡8(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1−559104acos⁡12(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1−2160acos⁡4(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1−294912acos⁡16(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1+65536acos⁡18(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1+81acos⁡2(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1+552960acos⁡14(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1+22176acos⁡6(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1+329472acos⁡10(1)−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1−1−559104asin⁡12(1)−114048asin⁡8(1)−294912asin⁡16(1)−2160asin⁡4(1)+81asin⁡2(1)+65536asin⁡18(1)+22176asin⁡6(1)+552960asin⁡14(1)+329472asin⁡10(1)−1−4tan⁡3(a)cot⁡4(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)+24tan⁡3(a)cot⁡2(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)−4tan⁡3(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)+4tan⁡(a)cot⁡4(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)−24tan⁡(a)cot⁡2(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)+4tan⁡(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(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{4 \tan^{3}{\left(a \right)} \cot^{4}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} + \frac{24 \tan^{3}{\left(a \right)} \cot^{2}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} - \frac{4 \tan^{3}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} + \frac{4 \tan{\left(a \right)} \cot^{4}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} - \frac{24 \tan{\left(a \right)} \cot^{2}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} + \frac{4 \tan{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} 
-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) - 4*tan(a)^3/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) + 4*tan(a)/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) - 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) - 24*cot(a)^2*tan(a)/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) - 4*cot(a)^4*tan(a)^3/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) + 4*cot(a)^4*tan(a)/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) + 24*cot(a)^2*tan(a)^3/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) + 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)
Denominador común [src] 
          2                       
-1 + a*cos (9)                    
-------------- + cot(4*a)*tan(4*a)
          2                       
-1 + a*sin (9)
tan⁡(4a)cot⁡(4a)+acos⁡2(9)−1asin⁡2(9)−1\tan{\left(4 a \right)} \cot{\left(4 a \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) + cot(4*a)*tan(4*a)
Parte trigonométrica [src] 
                                   2                       
               /       2/  9   pi\\                        
               |    csc |- - + --||                        
               |        \  2   2 /|                        
               |1 + --------------| *(-2 + a)              
               |         2        |                        
               \      csc (9/2)   /                        
-----------------------------------------------------------
        4/  9   pi\        2/  9   pi\          2/  9   pi\
     csc |- - + --|   2*csc |- - + --|   4*a*csc |- - + --|
         \  2   2 /         \  2   2 /           \  2   2 /
-1 - -------------- - ---------------- + ------------------
          4                 2                   2          
       csc (9/2)         csc (9/2)           csc (9/2)
(1+csc⁡2(−92+π2)csc⁡2(92))2(a−2)4acsc⁡2(−92+π2)csc⁡2(92)−csc⁡4(−92+π2)csc⁡4(92)−2csc⁡2(−92+π2)csc⁡2(92)−1\frac{\left(1 + \frac{\csc^{2}{\left(- \frac{9}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{9}{2} \right)}}\right)^{2} \left(a - 2\right)}{\frac{4 a \csc^{2}{\left(- \frac{9}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{9}{2} \right)}} - \frac{\csc^{4}{\left(- \frac{9}{2} + \frac{\pi}{2} \right)}}{\csc^{4}{\left(\frac{9}{2} \right)}} - \frac{2 \csc^{2}{\left(- \frac{9}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{9}{2} \right)}} - 1} 
             2    
    1 - a*cos (9) 
1 - --------------
              2   
    -1 + a*sin (9)
1−−acos⁡2(9)+1asin⁡2(9)−11 - \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1} 
              a      
       1 - -------   
              2      
           sec (9)   
1 - -----------------
              a      
    -1 + ------------
            2/    pi\
         sec |9 - --|
             \    2 /
−−asec⁡2(9)+1asec⁡2(9−π2)−1+1- \frac{- \frac{a}{\sec^{2}{\left(9 \right)}} + 1}{\frac{a}{\sec^{2}{\left(9 - \frac{\pi}{2} \right)}} - 1} + 1 
                        2                   
         /       2     \                    
         \1 + tan (9/2)/ *(-2 + a)          
--------------------------------------------
        4             2               2     
-1 - tan (9/2) - 2*tan (9/2) + 4*a*tan (9/2)
(1+tan⁡2(92))2(a−2)4atan⁡2(92)−tan⁡4(92)−2tan⁡2(92)−1\frac{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2} \left(a - 2\right)}{4 a \tan^{2}{\left(\frac{9}{2} \right)} - \tan^{4}{\left(\frac{9}{2} \right)} - 2 \tan^{2}{\left(\frac{9}{2} \right)} - 1} 
                          2                  
         /         4     \                   
         |    4*sin (9/2)|                   
         |1 + -----------| *(-2 + a)         
         |         2     |                   
         \      sin (9)  /                   
---------------------------------------------
                      4                4     
        4        8*sin (9/2)   16*a*sin (9/2)
-1 - tan (9/2) - ----------- + --------------
                      2              2       
                   sin (9)        sin (9)
(1+4sin⁡4(92)sin⁡2(9))2(a−2)16asin⁡4(92)sin⁡2(9)−tan⁡4(92)−8sin⁡4(92)sin⁡2(9)−1\frac{\left(1 + \frac{4 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}}\right)^{2} \left(a - 2\right)}{\frac{16 a \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}} - \tan^{4}{\left(\frac{9}{2} \right)} - \frac{8 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}} - 1} 
      2*(2 - a)       
----------------------
             /     pi\
2 - a + a*sin|18 + --|
             \     2 /
2(2−a)−a+asin⁡(π2+18)+2\frac{2 \left(2 - a\right)}{- a + a \sin{\left(\frac{\pi}{2} + 18 \right)} + 2} 
      -2 + a     
-----------------
          a      
-1 + ------------
        2/    pi\
     sec |9 - --|
         \    2 /
a−2asec⁡2(9−π2)−1\frac{a - 2}{\frac{a}{\sec^{2}{\left(9 - \frac{\pi}{2} \right)}} - 1} 
     4 - 2*a     
-----------------
2 - a + a*cos(18)
4−2a−a+acos⁡(18)+2\frac{4 - 2 a}{- a + a \cos{\left(18 \right)} + 2} 
       2*(2 - a)        
------------------------
          /        2   \
        a*\-1 + cot (9)/
2 - a + ----------------
                 2      
          1 + cot (9)
2(2−a)−a+a(−1+cot⁡2(9))1+cot⁡2(9)+2\frac{2 \left(2 - a\right)}{- a + \frac{a \left(-1 + \cot^{2}{\left(9 \right)}\right)}{1 + \cot^{2}{\left(9 \right)}} + 2} 
                2      
       1 - a*cos (9)   
1 - -------------------
              2/    pi\
    -1 + a*cos |9 - --|
               \    2 /
−−acos⁡2(9)+1acos⁡2(9−π2)−1+1- \frac{- a \cos^{2}{\left(9 \right)} + 1}{a \cos^{2}{\left(9 - \frac{\pi}{2} \right)} - 1} + 1 
        -2 + a       
---------------------
             2       
      4*a*cot (9/2)  
-1 + ----------------
                    2
     /       2     \ 
     \1 + cot (9/2)/
a−24acot⁡2(92)(cot⁡2(92)+1)2−1\frac{a - 2}{\frac{4 a \cot^{2}{\left(\frac{9}{2} \right)}}{\left(\cot^{2}{\left(\frac{9}{2} \right)} + 1\right)^{2}} - 1} 
        -2 + a       
---------------------
             2       
      4*a*tan (9/2)  
-1 + ----------------
                    2
     /       2     \ 
     \1 + tan (9/2)/
a−24atan⁡2(92)(1+tan⁡2(92))2−1\frac{a - 2}{\frac{4 a \tan^{2}{\left(\frac{9}{2} \right)}}{\left(1 + \tan^{2}{\left(\frac{9}{2} \right)}\right)^{2}} - 1} 
                            2                   
          /        2       \                    
          |     sec (9/2)  |                    
          |1 + ------------| *(-2 + a)          
          |       2/9   pi\|                    
          |    sec |- - --||                    
          \        \2   2 //                    
------------------------------------------------
         4               2                2     
      sec (9/2)     2*sec (9/2)    4*a*sec (9/2)
-1 - ------------ - ------------ + -------------
        4/9   pi\      2/9   pi\       2/9   pi\
     sec |- - --|   sec |- - --|    sec |- - --|
         \2   2 /       \2   2 /        \2   2 /
(1+sec⁡2(92)sec⁡2(92−π2))2(a−2)4asec⁡2(92)sec⁡2(92−π2)−sec⁡4(92)sec⁡4(92−π2)−2sec⁡2(92)sec⁡2(92−π2)−1\frac{\left(1 + \frac{\sec^{2}{\left(\frac{9}{2} \right)}}{\sec^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}\right)^{2} \left(a - 2\right)}{\frac{4 a \sec^{2}{\left(\frac{9}{2} \right)}}{\sec^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}} - \frac{\sec^{4}{\left(\frac{9}{2} \right)}}{\sec^{4}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}} - \frac{2 \sec^{2}{\left(\frac{9}{2} \right)}}{\sec^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}} - 1} 
    2*(2 - a)    
-----------------
2 - a + a*cos(18)
2(2−a)−a+acos⁡(18)+2\frac{2 \left(2 - a\right)}{- a + a \cos{\left(18 \right)} + 2} 
                         2
          /       2     \ 
        a*\1 - tan (9/2)/ 
    1 - ------------------
                        2 
         /       2     \  
         \1 + tan (9/2)/  
1 - ----------------------
                 2        
          4*a*tan (9/2)   
    -1 + ---------------- 
                        2 
         /       2     \  
         \1 + tan (9/2)/
−−a(1−tan⁡2(92))2(1+tan⁡2(92))2+14atan⁡2(92)(1+tan⁡2(92))2−1+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} + 1 
                          -8 + 4*a                          
------------------------------------------------------------
              /                      2               2     \
            2 |        4        4*sin (9/2)   8*a*sin (9/2)|
(1 + cos(9)) *|-1 - tan (9/2) - ----------- + -------------|
              \                  1 + cos(9)     1 + cos(9) /
4a−8(cos⁡(9)+1)2(8asin⁡2(92)cos⁡(9)+1−tan⁡4(92)−4sin⁡2(92)cos⁡(9)+1−1)\frac{4 a - 8}{\left(\cos{\left(9 \right)} + 1\right)^{2} \left(\frac{8 a \sin^{2}{\left(\frac{9}{2} \right)}}{\cos{\left(9 \right)} + 1} - \tan^{4}{\left(\frac{9}{2} \right)} - \frac{4 \sin^{2}{\left(\frac{9}{2} \right)}}{\cos{\left(9 \right)} + 1} - 1\right)} 
   -2 + a   
------------
        a   
-1 + -------
        2   
     csc (9)
a−2acsc⁡2(9)−1\frac{a - 2}{\frac{a}{\csc^{2}{\left(9 \right)}} - 1} 
              a      
    1 - -------------
           2/     pi\
        csc |-9 + --|
            \     2 /
1 - -----------------
               a     
       -1 + -------  
               2     
            csc (9)
1−−acsc⁡2(−9+π2)+1acsc⁡2(9)−11 - \frac{- \frac{a}{\csc^{2}{\left(-9 + \frac{\pi}{2} \right)}} + 1}{\frac{a}{\csc^{2}{\left(9 \right)}} - 1} 
                           2                    
          /         4     \                     
          |    4*sin (9/2)|                     
          |1 + -----------| *(-2 + a)           
          |         2     |                     
          \      sin (9)  /                     
------------------------------------------------
           8             4                4     
     16*sin (9/2)   8*sin (9/2)   16*a*sin (9/2)
-1 - ------------ - ----------- + --------------
          4              2              2       
       sin (9)        sin (9)        sin (9)
(1+4sin⁡4(92)sin⁡2(9))2(a−2)16asin⁡4(92)sin⁡2(9)−16sin⁡8(92)sin⁡4(9)−8sin⁡4(92)sin⁡2(9)−1\frac{\left(1 + \frac{4 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}}\right)^{2} \left(a - 2\right)}{\frac{16 a \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}} - \frac{16 \sin^{8}{\left(\frac{9}{2} \right)}}{\sin^{4}{\left(9 \right)}} - \frac{8 \sin^{4}{\left(\frac{9}{2} \right)}}{\sin^{2}{\left(9 \right)}} - 1} 
                               2                     
             /       2/9   pi\\                      
             |    cos |- - --||                      
             |        \2   2 /|                      
             |1 + ------------| *(-2 + a)            
             |        2       |                      
             \     cos (9/2)  /                      
-----------------------------------------------------
        4/9   pi\        2/9   pi\          2/9   pi\
     cos |- - --|   2*cos |- - --|   4*a*cos |- - --|
         \2   2 /         \2   2 /           \2   2 /
-1 - ------------ - -------------- + ----------------
         4               2                 2         
      cos (9/2)       cos (9/2)         cos (9/2)
(1+cos⁡2(92−π2)cos⁡2(92))2(a−2)4acos⁡2(92−π2)cos⁡2(92)−cos⁡4(92−π2)cos⁡4(92)−2cos⁡2(92−π2)cos⁡2(92)−1\frac{\left(1 + \frac{\cos^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{9}{2} \right)}}\right)^{2} \left(a - 2\right)}{\frac{4 a \cos^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{9}{2} \right)}} - \frac{\cos^{4}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}{\cos^{4}{\left(\frac{9}{2} \right)}} - \frac{2 \cos^{2}{\left(\frac{9}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{9}{2} \right)}} - 1} 
       2*(2 - a)       
-----------------------
          /       2   \
        a*\1 - tan (9)/
2 - a + ---------------
                 2     
          1 + tan (9)
2(2−a)−a+a(1−tan⁡2(9))tan⁡2(9)+1+2\frac{2 \left(2 - a\right)}{- 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     \  
          \1 + cot (9/2)/  
1 - -----------------------
                  2        
           4*a*cot (9/2)   
     -1 + ---------------- 
                         2 
          /       2     \  
          \1 + cot (9/2)/
−−a(−1+cot⁡2(92))2(cot⁡2(92)+1)2+14acot⁡2(92)(cot⁡2(92)+1)2−1+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} + 1 
   2*(2 - a)   
---------------
           a   
2 - a + -------
        sec(18)
2(2−a)−a+asec⁡(18)+2\frac{2 \left(2 - a\right)}{- a + \frac{a}{\sec{\left(18 \right)}} + 2} 
      2*(2 - a)      
---------------------
              a      
2 - a + -------------
           /      pi\
        csc|-18 + --|
           \      2 /
2(2−a)−a+acsc⁡(−18+π2)+2\frac{2 \left(2 - a\right)}{- a + \frac{a}{\csc{\left(-18 + \frac{\pi}{2} \right)}} + 2} 
             2/    pi\
    1 - a*sin |9 + --|
              \    2 /
1 - ------------------
                2     
      -1 + a*sin (9)
1−−asin⁡2(π2+9)+1asin⁡2(9)−11 - \frac{- a \sin^{2}{\left(\frac{\pi}{2} + 9 \right)} + 1}{a \sin^{2}{\left(9 \right)} - 1} 
    -2 + a    
--------------
          2   
-1 + a*sin (9)
a−2asin⁡2(9)−1\frac{a - 2}{a \sin^{2}{\left(9 \right)} - 1} 
       -2 + a       
--------------------
     a*(1 - cos(18))
-1 + ---------------
            2
a−2a(1−cos⁡(18))2−1\frac{a - 2}{\frac{a \left(1 - \cos{\left(18 \right)}\right)}{2} - 1} 
                     2                
      /        1    \                 
      |1 + ---------| *(-2 + a)       
      |       2     |                 
      \    cot (9/2)/                 
--------------------------------------
         1           2          4*a   
-1 - --------- - --------- + ---------
        4           2           2     
     cot (9/2)   cot (9/2)   cot (9/2)
(1+1cot⁡2(92))2(a−2)4acot⁡2(92)−1cot⁡4(92)−2cot⁡2(92)−1\frac{\left(1 + \frac{1}{\cot^{2}{\left(\frac{9}{2} \right)}}\right)^{2} \left(a - 2\right)}{\frac{4 a}{\cot^{2}{\left(\frac{9}{2} \right)}} - \frac{1}{\cot^{4}{\left(\frac{9}{2} \right)}} - \frac{2}{\cot^{2}{\left(\frac{9}{2} \right)}} - 1} 
           a    
    1 - ------- 
           2    
        sec (9) 
1 - ------------
            a   
    -1 + -------
            2   
         csc (9)
1−−asec⁡2(9)+1acsc⁡2(9)−11 - \frac{- \frac{a}{\sec^{2}{\left(9 \right)}} + 1}{\frac{a}{\csc^{2}{\left(9 \right)}} - 1} 
       -2 + a      
-------------------
          2/    pi\
-1 + a*cos |9 - --|
           \    2 /
a−2acos⁡2(9−π2)−1\frac{a - 2}{a \cos^{2}{\left(9 - \frac{\pi}{2} \right)} - 1} 
(-2 + a)/(-1 + a*cos(9 - pi/2)^2)
    © Sr Examen – Калькулятор