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

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

Expresión a simplificar:

Solución

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