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

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

Expresión a simplificar:

Solución

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