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

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

Expresión a simplificar:

Solución

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