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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(2*x)/((2*cos(x)))

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

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(2*x)
--------
2*cos(x)
$$\frac{\sin{\left(2 x \right)}}{2 \cos{\left(x \right)}}$$ 
sin(2*x)/((2*cos(x)))
Simplificación general [src] 
sin(x)
$$\sin{\left(x \right)}$$ 
sin(x)
Respuesta numérica [src] 
0.5*sin(2*x)/cos(x)
0.5*sin(2*x)/cos(x)
Potencias [src] 
   /   -2*I*x    2*I*x\ 
-I*\- e       + e     / 
------------------------
      / I*x    -I*x\    
    2*\e    + e    /
$$- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(e^{i x} + e^{- i x}\right)}$$ 
-i*(-exp(-2*i*x) + exp(2*i*x))/(2*(exp(i*x) + exp(-i*x)))
Abrimos la expresión [src] 
sin(x)
$$\sin{\left(x \right)}$$ 
sin(x)
Parte trigonométrica [src] 
   /pi    \
csc|-- - x|
   \2     /
-----------
 2*csc(2*x)
$$\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{2 \csc{\left(2 x \right)}}$$ 
  sec(x)  
----------
2*csc(2*x)
$$\frac{\sec{\left(x \right)}}{2 \csc{\left(2 x \right)}}$$ 
     1     
-----------
   /    pi\
sec|x - --|
   \    2 /
$$\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}$$ 
    /       2/x\\          
    |1 + tan |-||*tan(x)   
    \        \2//          
---------------------------
/       2   \ /       2/x\\
\1 + tan (x)/*|1 - tan |-||
              \        \2//
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(x \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}$$ 
   /    pi\
cos|x - --|
   \    2 /
$$\cos{\left(x - \frac{\pi}{2} \right)}$$ 
       /x\ 
  2*cot|-| 
       \2/ 
-----------
       2/x\
1 + cot |-|
        \2/
$$\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}$$ 
   /      pi\
cos|2*x - --|
   \      2 /
-------------
   2*cos(x)
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{2 \cos{\left(x \right)}}$$ 
   sin(2*x)  
-------------
     /    pi\
2*sin|x + --|
     \    2 /
$$\frac{\sin{\left(2 x \right)}}{2 \sin{\left(x + \frac{\pi}{2} \right)}}$$ 
  1   
------
csc(x)
$$\frac{1}{\csc{\left(x \right)}}$$ 
       /x\ 
  2*tan|-| 
       \2/ 
-----------
       2/x\
1 + tan |-|
        \2/
$$\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$ 
sin(x)
$$\sin{\left(x \right)}$$ 
    /       2/x\\           
    |1 + cot |-||*cot(x)    
    \        \2//           
----------------------------
/       2   \ /        2/x\\
\1 + cot (x)/*|-1 + cot |-||
              \         \2//
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}$$ 
     sec(x)    
---------------
     /      pi\
2*sec|2*x - --|
     \      2 /
$$\frac{\sec{\left(x \right)}}{2 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$ 
sec(x)/(2*sec(2*x - pi/2))
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