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Simplificación de expresiones/ Descomposición en fracciones simples/ tan2αc2α-(1-sin^25α)/(cos^25α-1)

¿Cómo vas a descomponer esta tan2αc2α-(1-sin^25α)/(cos^25α-1) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                       25   
                1 - sin  (a)
tan(2*a)*c2*a - ------------
                   25       
                cos  (a) - 1
$$a c_{2} \tan{\left(2 a \right)} - \frac{1 - \sin^{25}{\left(a \right)}}{\cos^{25}{\left(a \right)} - 1}$$ 
(tan(2*a)*c2)*a - (1 - sin(a)^25)/(cos(a)^25 - 1)
Simplificación general [src] 
        25           /        25   \         
-1 + sin  (a) + a*c2*\-1 + cos  (a)/*tan(2*a)
---------------------------------------------
                        25                   
                -1 + cos  (a)
$$\frac{a c_{2} \left(\cos^{25}{\left(a \right)} - 1\right) \tan{\left(2 a \right)} + \sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$ 
(-1 + sin(a)^25 + a*c2*(-1 + cos(a)^25)*tan(2*a))/(-1 + cos(a)^25)
Denominador común [src] 
        25                   
-1 + sin  (a)                
------------- + a*c2*tan(2*a)
        25                   
-1 + cos  (a)
$$a c_{2} \tan{\left(2 a \right)} + \frac{\sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$ 
(-1 + sin(a)^25)/(-1 + cos(a)^25) + a*c2*tan(2*a)
Unión de expresiones racionales [src] 
        25           /        25   \         
-1 + sin  (a) + a*c2*\-1 + cos  (a)/*tan(2*a)
---------------------------------------------
                        25                   
                -1 + cos  (a)
$$\frac{a c_{2} \left(\cos^{25}{\left(a \right)} - 1\right) \tan{\left(2 a \right)} + \sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$ 
(-1 + sin(a)^25 + a*c2*(-1 + cos(a)^25)*tan(2*a))/(-1 + cos(a)^25)
Denominador racional [src] 
        25           /        25   \         
-1 + sin  (a) + a*c2*\-1 + cos  (a)/*tan(2*a)
---------------------------------------------
                        25                   
                -1 + cos  (a)
$$\frac{a c_{2} \left(\cos^{25}{\left(a \right)} - 1\right) \tan{\left(2 a \right)} + \sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$ 
(-1 + sin(a)^25 + a*c2*(-1 + cos(a)^25)*tan(2*a))/(-1 + cos(a)^25)
Respuesta numérica [src] 
-(1.0 - sin(a)^25)/(-1.0 + cos(a)^25) + a*c2*tan(2*a)
-(1.0 - sin(a)^25)/(-1.0 + cos(a)^25) + a*c2*tan(2*a)
Potencias [src] 
                        25                              
        /   -I*a    I*a\                                
      I*\- e     + e   /                                
  1 + --------------------          /   2*I*a    -2*I*a\
            33554432         I*a*c2*\- e      + e      /
- ------------------------ + ---------------------------
                      25            -2*I*a    2*I*a     
        / I*a    -I*a\             e       + e          
        |e      e    |                                  
   -1 + |---- + -----|                                  
        \ 2       2  /
$$\frac{i a c_{2} \left(- e^{2 i a} + e^{- 2 i a}\right)}{e^{2 i a} + e^{- 2 i a}} - \frac{\frac{i \left(e^{i a} - e^{- i a}\right)^{25}}{33554432} + 1}{\left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{25} - 1}$$ 
        25                   
-1 + sin  (a)                
------------- + a*c2*tan(2*a)
        25                   
-1 + cos  (a)
$$a c_{2} \tan{\left(2 a \right)} + \frac{\sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$ 
(-1 + sin(a)^25)/(-1 + cos(a)^25) + a*c2*tan(2*a)
Combinatoria [src] 
                                 25                              25                                    
                         -1 + sin  (a) - a*c2*tan(2*a) + a*c2*cos  (a)*tan(2*a)                        
-------------------------------------------------------------------------------------------------------
              /       2         3         4            \ /       5         10         15         20   \
(-1 + cos(a))*\1 + cos (a) + cos (a) + cos (a) + cos(a)/*\1 + cos (a) + cos  (a) + cos  (a) + cos  (a)/
$$\frac{a c_{2} \cos^{25}{\left(a \right)} \tan{\left(2 a \right)} - a c_{2} \tan{\left(2 a \right)} + \sin^{25}{\left(a \right)} - 1}{\left(\cos{\left(a \right)} - 1\right) \left(\cos^{4}{\left(a \right)} + \cos^{3}{\left(a \right)} + \cos^{2}{\left(a \right)} + \cos{\left(a \right)} + 1\right) \left(\cos^{20}{\left(a \right)} + \cos^{15}{\left(a \right)} + \cos^{10}{\left(a \right)} + \cos^{5}{\left(a \right)} + 1\right)}$$ 
(-1 + sin(a)^25 - a*c2*tan(2*a) + a*c2*cos(a)^25*tan(2*a))/((-1 + cos(a))*(1 + cos(a)^2 + cos(a)^3 + cos(a)^4 + cos(a))*(1 + cos(a)^5 + cos(a)^10 + cos(a)^15 + cos(a)^20))
Abrimos la expresión [src] 
                      25                     
       1           sin  (a)     2*a*c2*tan(a)
- ------------ + ------------ + -------------
     25             25                  2    
  cos  (a) - 1   cos  (a) - 1    1 - tan (a)
$$\frac{2 a c_{2} \tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}} + \frac{\sin^{25}{\left(a \right)}}{\cos^{25}{\left(a \right)} - 1} - \frac{1}{\cos^{25}{\left(a \right)} - 1}$$ 
-1/(cos(a)^25 - 1) + sin(a)^25/(cos(a)^25 - 1) + 2*a*c2*tan(a)/(1 - tan(a)^2)
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