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Simplificación de expresiones/ Descomposición en fracciones simples/ tg4a*tg4a-(1-cos^29a)/(sin^29a)

¿Cómo vas a descomponer esta tg4a*tg4a-(1-cos^29a)/(sin^29a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                           29   
                    1 - cos  (a)
tan(4*a)*tan(4*a) - ------------
                         29     
                      sin  (a)
−1−cos⁡29(a)sin⁡29(a)+tan⁡(4a)tan⁡(4a)- \frac{1 - \cos^{29}{\left(a \right)}}{\sin^{29}{\left(a \right)}} + \tan{\left(4 a \right)} \tan{\left(4 a \right)} 
tan(4*a)*tan(4*a) - (1 - cos(a)^29)/sin(a)^29
Simplificación general [src] 
   1          2           1    
-------- + tan (4*a) - --------
   29                     29   
tan  (a)               sin  (a)
tan⁡2(4a)+1tan⁡29(a)−1sin⁡29(a)\tan^{2}{\left(4 a \right)} + \frac{1}{\tan^{29}{\left(a \right)}} - \frac{1}{\sin^{29}{\left(a \right)}} 
tan(a)^(-29) + tan(4*a)^2 - 1/sin(a)^29
Potencias [src] 
                   29   
   2        1 - cos  (a)
tan (4*a) - ------------
                 29     
              sin  (a)
−1−cos⁡29(a)sin⁡29(a)+tan⁡2(4a)- \frac{1 - \cos^{29}{\left(a \right)}}{\sin^{29}{\left(a \right)}} + \tan^{2}{\left(4 a \right)} 
                    29   
   2        -1 + cos  (a)
tan (4*a) + -------------
                  29     
               sin  (a)
cos⁡29(a)−1sin⁡29(a)+tan⁡2(4a)\frac{\cos^{29}{\left(a \right)} - 1}{\sin^{29}{\left(a \right)}} + \tan^{2}{\left(4 a \right)} 
                                      /                  29\
                                      |    / I*a    -I*a\  |
                      2               |    |e      e    |  |
  /   4*I*a    -4*I*a\    536870912*I*|1 - |---- + -----|  |
  \- e      + e      /                \    \ 2       2  /  /
- --------------------- - ----------------------------------
                     2                            29        
   / -4*I*a    4*I*a\             /   -I*a    I*a\          
   \e       + e     /             \- e     + e   /
−536870912i(1−(eia2+e−ia2)29)(eia−e−ia)29−(−e4ia+e−4ia)2(e4ia+e−4ia)2- \frac{536870912 i \left(1 - \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{29}\right)}{\left(e^{i a} - e^{- i a}\right)^{29}} - \frac{\left(- e^{4 i a} + e^{- 4 i a}\right)^{2}}{\left(e^{4 i a} + e^{- 4 i a}\right)^{2}} 
-(-exp(4*i*a) + exp(-4*i*a))^2/(exp(-4*i*a) + exp(4*i*a))^2 - 536870912*i*(1 - (exp(i*a)/2 + exp(-i*a)/2)^29)/(-exp(-i*a) + exp(i*a))^29
Unión de expresiones racionales [src] 
        29         29       2     
-1 + cos  (a) + sin  (a)*tan (4*a)
----------------------------------
                29                
             sin  (a)
sin⁡29(a)tan⁡2(4a)+cos⁡29(a)−1sin⁡29(a)\frac{\sin^{29}{\left(a \right)} \tan^{2}{\left(4 a \right)} + \cos^{29}{\left(a \right)} - 1}{\sin^{29}{\left(a \right)}} 
(-1 + cos(a)^29 + sin(a)^29*tan(4*a)^2)/sin(a)^29
Compilar la expresión [src] 
                   29   
   2        1 - cos  (a)
tan (4*a) - ------------
                 29     
              sin  (a)
−1−cos⁡29(a)sin⁡29(a)+tan⁡2(4a)- \frac{1 - \cos^{29}{\left(a \right)}}{\sin^{29}{\left(a \right)}} + \tan^{2}{\left(4 a \right)} 
tan(4*a)^2 - (1 - cos(a)^29)/sin(a)^29
Abrimos la expresión [src] 
                29                                4                                                    2                                                    6                       
     1       cos  (a)                       32*tan (a)                                           16*tan (a)                                           16*tan (a)                    
- -------- + -------- - -------------------------------------------------- + -------------------------------------------------- + --------------------------------------------------
     29         29             8            2            6            4             8            2            6            4             8            2            6            4   
  sin  (a)   sin  (a)   1 + tan (a) - 12*tan (a) - 12*tan (a) + 38*tan (a)   1 + tan (a) - 12*tan (a) - 12*tan (a) + 38*tan (a)   1 + tan (a) - 12*tan (a) - 12*tan (a) + 38*tan (a)
cos⁡29(a)sin⁡29(a)−1sin⁡29(a)+16tan⁡6(a)tan⁡8(a)−12tan⁡6(a)+38tan⁡4(a)−12tan⁡2(a)+1−32tan⁡4(a)tan⁡8(a)−12tan⁡6(a)+38tan⁡4(a)−12tan⁡2(a)+1+16tan⁡2(a)tan⁡8(a)−12tan⁡6(a)+38tan⁡4(a)−12tan⁡2(a)+1\frac{\cos^{29}{\left(a \right)}}{\sin^{29}{\left(a \right)}} - \frac{1}{\sin^{29}{\left(a \right)}} + \frac{16 \tan^{6}{\left(a \right)}}{\tan^{8}{\left(a \right)} - 12 \tan^{6}{\left(a \right)} + 38 \tan^{4}{\left(a \right)} - 12 \tan^{2}{\left(a \right)} + 1} - \frac{32 \tan^{4}{\left(a \right)}}{\tan^{8}{\left(a \right)} - 12 \tan^{6}{\left(a \right)} + 38 \tan^{4}{\left(a \right)} - 12 \tan^{2}{\left(a \right)} + 1} + \frac{16 \tan^{2}{\left(a \right)}}{\tan^{8}{\left(a \right)} - 12 \tan^{6}{\left(a \right)} + 38 \tan^{4}{\left(a \right)} - 12 \tan^{2}{\left(a \right)} + 1} 
-1/sin(a)^29 + cos(a)^29/sin(a)^29 - 32*tan(a)^4/(1 + tan(a)^8 - 12*tan(a)^2 - 12*tan(a)^6 + 38*tan(a)^4) + 16*tan(a)^2/(1 + tan(a)^8 - 12*tan(a)^2 - 12*tan(a)^6 + 38*tan(a)^4) + 16*tan(a)^6/(1 + tan(a)^8 - 12*tan(a)^2 - 12*tan(a)^6 + 38*tan(a)^4)
Denominador racional [src] 
        29         29       2     
-1 + cos  (a) + sin  (a)*tan (4*a)
----------------------------------
                29                
             sin  (a)
sin⁡29(a)tan⁡2(4a)+cos⁡29(a)−1sin⁡29(a)\frac{\sin^{29}{\left(a \right)} \tan^{2}{\left(4 a \right)} + \cos^{29}{\left(a \right)} - 1}{\sin^{29}{\left(a \right)}} 
(-1 + cos(a)^29 + sin(a)^29*tan(4*a)^2)/sin(a)^29
Denominador común [src] 
                    29   
   2        -1 + cos  (a)
tan (4*a) + -------------
                  29     
               sin  (a)
cos⁡29(a)−1sin⁡29(a)+tan⁡2(4a)\frac{\cos^{29}{\left(a \right)} - 1}{\sin^{29}{\left(a \right)}} + \tan^{2}{\left(4 a \right)} 
tan(4*a)^2 + (-1 + cos(a)^29)/sin(a)^29
Respuesta numérica [src] 
tan(4*a)^2 - (1.0 - cos(a)^29)/sin(a)^29
tan(4*a)^2 - (1.0 - cos(a)^29)/sin(a)^29
Combinatoria [src] 
        29         29       2     
-1 + cos  (a) + sin  (a)*tan (4*a)
----------------------------------
                29                
             sin  (a)
sin⁡29(a)tan⁡2(4a)+cos⁡29(a)−1sin⁡29(a)\frac{\sin^{29}{\left(a \right)} \tan^{2}{\left(4 a \right)} + \cos^{29}{\left(a \right)} - 1}{\sin^{29}{\left(a \right)}} 
(-1 + cos(a)^29 + sin(a)^29*tan(4*a)^2)/sin(a)^29
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