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¿Cómo vas a descomponer esta sin(p+a)^2+sin(p/(2+a))^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
   2             2/  p  \
sin (p + a) + sin |-----|
                  \2 + a/
$$\sin^{2}{\left(\frac{p}{a + 2} \right)} + \sin^{2}{\left(a + p \right)}$$
sin(p + a)^2 + sin(p/(2 + a))^2
Potencias [src]
                                                     2
                                  /   -I*p      I*p \ 
                              2   |   -----    -----| 
  /   I*(-a - p)    I*(a + p)\    |   2 + a    2 + a| 
  \- e           + e         /    \- e      + e     / 
- ----------------------------- - --------------------
                4                          4          
$$- \frac{\left(- e^{i \left(- a - p\right)} + e^{i \left(a + p\right)}\right)^{2}}{4} - \frac{\left(e^{\frac{i p}{a + 2}} - e^{- \frac{i p}{a + 2}}\right)^{2}}{4}$$
-(-exp(i*(-a - p)) + exp(i*(a + p)))^2/4 - (-exp(-i*p/(2 + a)) + exp(i*p/(2 + a)))^2/4
Abrimos la expresión [src]
   2/  p  \      2       2         2       2                                   
sin |-----| + cos (a)*sin (p) + cos (p)*sin (a) + 2*cos(a)*cos(p)*sin(a)*sin(p)
    \2 + a/                                                                    
$$\sin^{2}{\left(a \right)} \cos^{2}{\left(p \right)} + 2 \sin{\left(a \right)} \sin{\left(p \right)} \cos{\left(a \right)} \cos{\left(p \right)} + \sin^{2}{\left(p \right)} \cos^{2}{\left(a \right)} + \sin^{2}{\left(\frac{p}{a + 2} \right)}$$
sin(p/(2 + a))^2 + cos(a)^2*sin(p)^2 + cos(p)^2*sin(a)^2 + 2*cos(a)*cos(p)*sin(a)*sin(p)
Respuesta numérica [src]
sin(p/(2 + a))^2 + sin(p + a)^2
sin(p/(2 + a))^2 + sin(p + a)^2