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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(a+b)*b/((cos(a)*cos(b)))+tan(b)

¿Cómo vas a descomponer esta sin(a+b)*b/((cos(a)*cos(b)))+tan(b) expresión en fracciones?

Expresión a simplificar:

Solución

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