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Simplificación de expresiones/ Descomposición en fracciones simples/ tan(3*n/2)*tan(n+a)-cos(n/(2+a))*sin(n+a)

¿Cómo vas a descomponer esta tan(3*n/2)*tan(n+a)-cos(n/(2+a))*sin(n+a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   /3*n\                 /  n  \           
tan|---|*tan(n + a) - cos|-----|*sin(n + a)
   \ 2 /                 \2 + a/
$$- \sin{\left(a + n \right)} \cos{\left(\frac{n}{a + 2} \right)} + \tan{\left(\frac{3 n}{2} \right)} \tan{\left(a + n \right)}$$ 
tan((3*n)/2)*tan(n + a) - cos(n/(2 + a))*sin(n + a)
Respuesta numérica [src] 
tan((3*n)/2)*tan(n + a) - cos(n/(2 + a))*sin(n + a)
tan((3*n)/2)*tan(n + a) - cos(n/(2 + a))*sin(n + a)
Potencias [src] 
  /  I*n     -I*n \                                                                                 
  | -----    -----|                                                                                 
  | 2 + a    2 + a|                                                             /   3*I*n    -3*I*n\
  |e        e     | /   I*(-a - n)    I*(a + n)\                                |   -----    ------|
I*|------ + ------|*\- e           + e         /   /   I*(a + n)    I*(-a - n)\ |     2        2   |
  \  2        2   /                                \- e          + e          /*\- e      + e      /
------------------------------------------------ - -------------------------------------------------
                       2                                                        / -3*I*n    3*I*n\  
                                                                                | ------    -----|  
                                                     / I*(a + n)    I*(-a - n)\ |   2         2  |  
                                                     \e          + e          /*\e       + e     /
$$- \frac{\left(- e^{\frac{3 i n}{2}} + e^{- \frac{3 i n}{2}}\right) \left(e^{i \left(- a - n\right)} - e^{i \left(a + n\right)}\right)}{\left(e^{\frac{3 i n}{2}} + e^{- \frac{3 i n}{2}}\right) \left(e^{i \left(- a - n\right)} + e^{i \left(a + n\right)}\right)} + \frac{i \left(- e^{i \left(- a - n\right)} + e^{i \left(a + n\right)}\right) \left(\frac{e^{\frac{i n}{a + 2}}}{2} + \frac{e^{- \frac{i n}{a + 2}}}{2}\right)}{2}$$ 
i*(exp(i*n/(2 + a))/2 + exp(-i*n/(2 + a))/2)*(-exp(i*(-a - n)) + exp(i*(a + n)))/2 - (-exp(i*(a + n)) + exp(i*(-a - n)))*(-exp(3*i*n/2) + exp(-3*i*n/2))/((exp(i*(a + n)) + exp(i*(-a - n)))*(exp(-3*i*n/2) + exp(3*i*n/2)))
Abrimos la expresión [src] 
           /3*n\               /3*n\                                                       
 tan(a)*tan|---|     tan(n)*tan|---|                                                       
           \ 2 /               \ 2 /              /  n  \                    /  n  \       
----------------- + ----------------- - cos(a)*cos|-----|*sin(n) - cos(n)*cos|-----|*sin(a)
1 - tan(a)*tan(n)   1 - tan(a)*tan(n)             \2 + a/                    \2 + a/
$$- \sin{\left(a \right)} \cos{\left(n \right)} \cos{\left(\frac{n}{a + 2} \right)} - \sin{\left(n \right)} \cos{\left(a \right)} \cos{\left(\frac{n}{a + 2} \right)} + \frac{\tan{\left(a \right)} \tan{\left(\frac{3 n}{2} \right)}}{- \tan{\left(a \right)} \tan{\left(n \right)} + 1} + \frac{\tan{\left(n \right)} \tan{\left(\frac{3 n}{2} \right)}}{- \tan{\left(a \right)} \tan{\left(n \right)} + 1}$$ 
tan(a)*tan(3*n/2)/(1 - tan(a)*tan(n)) + tan(n)*tan(3*n/2)/(1 - tan(a)*tan(n)) - cos(a)*cos(n/(2 + a))*sin(n) - cos(n)*cos(n/(2 + a))*sin(a)
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