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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   /p    \     cos(p + a) 
sin|- + a| - -------------
   \2    /   -sin(a - 2*p)
$$\sin{\left(a + \frac{p}{2} \right)} - \frac{\cos{\left(a + p \right)}}{\left(-1\right) \sin{\left(a - 2 p \right)}}$$ 
sin(p/2 + a) - cos(p + a)/((-sin(a - 2*p)))
Simplificación general [src] 
 cos(a + p)       /    p\
------------ + sin|a + -|
sin(a - 2*p)      \    2/
$$\sin{\left(a + \frac{p}{2} \right)} + \frac{\cos{\left(a + p \right)}}{\sin{\left(a - 2 p \right)}}$$ 
cos(a + p)/sin(a - 2*p) + sin(a + p/2)
Respuesta numérica [src] 
cos(p + a)/sin(a - 2*p) + sin(p/2 + a)
cos(p + a)/sin(a - 2*p) + sin(p/2 + a)
Denominador racional [src] 
                /    p\             
sin(a - 2*p)*sin|a + -| + cos(a + p)
                \    2/             
------------------------------------
            sin(a - 2*p)
$$\frac{\sin{\left(a - 2 p \right)} \sin{\left(a + \frac{p}{2} \right)} + \cos{\left(a + p \right)}}{\sin{\left(a - 2 p \right)}}$$ 
(sin(a - 2*p)*sin(a + p/2) + cos(a + p))/sin(a - 2*p)
Combinatoria [src] 
   /    p\                          
sin|a + -|*sin(a - 2*p) + cos(a + p)
   \    2/                          
------------------------------------
            sin(a - 2*p)
$$\frac{\sin{\left(a - 2 p \right)} \sin{\left(a + \frac{p}{2} \right)} + \cos{\left(a + p \right)}}{\sin{\left(a - 2 p \right)}}$$ 
(sin(a + p/2)*sin(a - 2*p) + cos(a + p))/sin(a - 2*p)
Abrimos la expresión [src] 
 cos(p + a)       /p    \
------------ + sin|- + a|
sin(a - 2*p)      \2    /
$$\sin{\left(a + \frac{p}{2} \right)} + \frac{\cos{\left(a + p \right)}}{\sin{\left(a - 2 p \right)}}$$ 
          /p\      /p\                             cos(a)*cos(p)                                         sin(a)*sin(p)                   
cos(a)*sin|-| + cos|-|*sin(a) + --------------------------------------------------- - ---------------------------------------------------
          \2/      \2/                         2                                                     2                                   
                                -sin(a) + 2*cos (p)*sin(a) - 2*cos(a)*cos(p)*sin(p)   -sin(a) + 2*cos (p)*sin(a) - 2*cos(a)*cos(p)*sin(p)
$$\sin{\left(a \right)} \cos{\left(\frac{p}{2} \right)} + \sin{\left(\frac{p}{2} \right)} \cos{\left(a \right)} - \frac{\sin{\left(a \right)} \sin{\left(p \right)}}{2 \sin{\left(a \right)} \cos^{2}{\left(p \right)} - \sin{\left(a \right)} - 2 \sin{\left(p \right)} \cos{\left(a \right)} \cos{\left(p \right)}} + \frac{\cos{\left(a \right)} \cos{\left(p \right)}}{2 \sin{\left(a \right)} \cos^{2}{\left(p \right)} - \sin{\left(a \right)} - 2 \sin{\left(p \right)} \cos{\left(a \right)} \cos{\left(p \right)}}$$ 
cos(a)*sin(p/2) + cos(p/2)*sin(a) + cos(a)*cos(p)/(-sin(a) + 2*cos(p)^2*sin(a) - 2*cos(a)*cos(p)*sin(p)) - sin(a)*sin(p)/(-sin(a) + 2*cos(p)^2*sin(a) - 2*cos(a)*cos(p)*sin(p))
Compilar la expresión [src] 
 cos(p + a)       /p    \
------------ + sin|- + a|
sin(a - 2*p)      \2    /
$$\sin{\left(a + \frac{p}{2} \right)} + \frac{\cos{\left(a + p \right)}}{\sin{\left(a - 2 p \right)}}$$ 
cos(p + a)/sin(a - 2*p) + sin(p/2 + a)
Unión de expresiones racionales [src] 
   /p + 2*a\                          
sin|-------|*sin(a - 2*p) + cos(a + p)
   \   2   /                          
--------------------------------------
             sin(a - 2*p)
$$\frac{\sin{\left(a - 2 p \right)} \sin{\left(\frac{2 a + p}{2} \right)} + \cos{\left(a + p \right)}}{\sin{\left(a - 2 p \right)}}$$ 
(sin((p + 2*a)/2)*sin(a - 2*p) + cos(a + p))/sin(a - 2*p)
Denominador común [src] 
 cos(a + p)       /    p\
------------ + sin|a + -|
sin(a - 2*p)      \    2/
$$\sin{\left(a + \frac{p}{2} \right)} + \frac{\cos{\left(a + p \right)}}{\sin{\left(a - 2 p \right)}}$$ 
cos(a + p)/sin(a - 2*p) + sin(a + p/2)
Potencias [src] 
    /     /     p\      /    p\\       / I*(a + p)    I*(-a - p)\
    |   I*|-a - -|    I*|a + -||       |e            e          |
    |     \     2/      \    2/|   2*I*|---------- + -----------|
  I*\- e           + e         /       \    2             2     /
- ------------------------------ + ------------------------------
                2                     I*(-a + 2*p)    I*(a - 2*p)
                                   - e             + e
$$\frac{2 i \left(\frac{e^{i \left(- a - p\right)}}{2} + \frac{e^{i \left(a + p\right)}}{2}\right)}{- e^{i \left(- a + 2 p\right)} + e^{i \left(a - 2 p\right)}} - \frac{i \left(- e^{i \left(- a - \frac{p}{2}\right)} + e^{i \left(a + \frac{p}{2}\right)}\right)}{2}$$ 
 cos(a + p)       /    p\
------------ + sin|a + -|
sin(a - 2*p)      \    2/
$$\sin{\left(a + \frac{p}{2} \right)} + \frac{\cos{\left(a + p \right)}}{\sin{\left(a - 2 p \right)}}$$ 
cos(a + p)/sin(a - 2*p) + sin(a + p/2)
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