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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(2*x)/(1+cos(2*x))

¿Cómo vas a descomponer esta sin(2*x)/(1+cos(2*x)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
  sin(2*x)  
------------
1 + cos(2*x)
sin⁡(2x)cos⁡(2x)+1\frac{\sin{\left(2 x \right)}}{\cos{\left(2 x \right)} + 1} 
sin(2*x)/(1 + cos(2*x))
Simplificación general [src] 
tan(x)
tan⁡(x)\tan{\left(x \right)} 
tan(x)
Respuesta numérica [src] 
sin(2*x)/(1.0 + cos(2*x))
sin(2*x)/(1.0 + cos(2*x))
Potencias [src] 
   /   -2*I*x    2*I*x\ 
-I*\- e       + e     / 
------------------------
  /     -2*I*x    2*I*x\
  |    e         e     |
2*|1 + ------- + ------|
  \       2        2   /
−i(e2ix−e−2ix)2(e2ix2+1+e−2ix2)- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(\frac{e^{2 i x}}{2} + 1 + \frac{e^{- 2 i x}}{2}\right)} 
-i*(-exp(-2*i*x) + exp(2*i*x))/(2*(1 + exp(-2*i*x)/2 + exp(2*i*x)/2))
Abrimos la expresión [src] 
sin(x)
------
cos(x)
sin⁡(x)cos⁡(x)\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} 
sin(x)/cos(x)
Parte trigonométrica [src] 
   /      pi\
cos|2*x - --|
   \      2 /
-------------
 1 + cos(2*x)
cos⁡(2x−π2)cos⁡(2x)+1\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos{\left(2 x \right)} + 1} 
            2*tan(x)           
-------------------------------
              /           2   \
/       2   \ |    1 - tan (x)|
\1 + tan (x)/*|1 + -----------|
              |           2   |
              \    1 + tan (x)/
2tan⁡(x)(1−tan⁡2(x)tan⁡2(x)+1+1)(tan⁡2(x)+1)\frac{2 \tan{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)} 
           1           
-----------------------
/       1    \         
|1 + --------|*csc(2*x)
\    sec(2*x)/
1(1+1sec⁡(2x))csc⁡(2x)\frac{1}{\left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \csc{\left(2 x \right)}} 
     2   
2*sin (x)
---------
 sin(2*x)
2sin⁡2(x)sin⁡(2x)\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} 
   /    pi\
cos|x - --|
   \    2 /
-----------
   cos(x)
cos⁡(x−π2)cos⁡(x)\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} 
  1   
------
cot(x)
1cot⁡(x)\frac{1}{\cot{\left(x \right)}} 
     sin(2*x)    
-----------------
       /pi      \
1 + sin|-- + 2*x|
       \2       /
sin⁡(2x)sin⁡(2x+π2)+1\frac{\sin{\left(2 x \right)}}{\sin{\left(2 x + \frac{\pi}{2} \right)} + 1} 
             1              
----------------------------
/       1    \    /      pi\
|1 + --------|*sec|2*x - --|
\    sec(2*x)/    \      2 /
1(1+1sec⁡(2x))sec⁡(2x−π2)\frac{1}{\left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}} 
            2*cot(x)            
--------------------------------
              /            2   \
/       2   \ |    -1 + cot (x)|
\1 + cot (x)/*|1 + ------------|
              |           2    |
              \    1 + cot (x) /
2cot⁡(x)(cot⁡2(x)−1cot⁡2(x)+1+1)(cot⁡2(x)+1)\frac{2 \cot{\left(x \right)}}{\left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)} 
   sec(x)  
-----------
   /    pi\
sec|x - --|
   \    2 /
sec⁡(x)sec⁡(x−π2)\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} 
tan(x)
tan⁡(x)\tan{\left(x \right)} 
   /pi    \
csc|-- - x|
   \2     /
-----------
   csc(x)
csc⁡(−x+π2)csc⁡(x)\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} 
             1              
----------------------------
/          1      \         
|1 + -------------|*csc(2*x)
|       /pi      \|         
|    csc|-- - 2*x||         
\       \2       //
1(1+1csc⁡(−2x+π2))csc⁡(2x)\frac{1}{\left(1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(2 x \right)}} 
1/((1 + 1/csc(pi/2 - 2*x))*csc(2*x))
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