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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(x+y)/(cosx*cosy)+tgy

¿Cómo vas a descomponer esta sin(x+y)/(cosx*cosy)+tgy expresión en fracciones?

Expresión a simplificar:

Solución

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