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Simplificación de expresiones/ Descomposición en fracciones simples/ (sin2x)/(2*cos^2x)

¿Cómo vas a descomponer esta (sin2x)/(2*cos^2x) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
 sin(2*x)
---------
     2   
2*cos (x)
sin⁡(2x)2cos⁡2(x)\frac{\sin{\left(2 x \right)}}{2 \cos^{2}{\left(x \right)}} 
sin(2*x)/((2*cos(x)^2))
Simplificación general [src] 
tan(x)
tan⁡(x)\tan{\left(x \right)} 
tan(x)
Respuesta numérica [src] 
0.5*sin(2*x)/cos(x)^2
0.5*sin(2*x)/cos(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       
    sec (x)    
---------------
     /      pi\
2*sec|2*x - --|
     \      2 /
sec⁡2(x)2sec⁡(2x−π2)\frac{\sec^{2}{\left(x \right)}}{2 \sec{\left(2 x - \frac{\pi}{2} \right)}} 
   /pi    \
csc|-- - x|
   \2     /
-----------
   csc(x)
csc⁡(−x+π2)csc⁡(x)\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \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)} 
   /    pi\
cos|x - --|
   \    2 /
-----------
   cos(x)
cos⁡(x−π2)cos⁡(x)\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\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} 
tan(x)
tan⁡(x)\tan{\left(x \right)} 
                 2           
    /       2/x\\            
    |1 + cot |-|| *cot(x)    
    \        \2//            
-----------------------------
                            2
/       2   \ /        2/x\\ 
\1 + cot (x)/*|-1 + cot |-|| 
              \         \2//
(cot⁡2(x2)+1)2cot⁡(x)(cot⁡2(x2)−1)2(cot⁡2(x)+1)\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \cot{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right)} 
   sin(2*x)   
--------------
     2/    pi\
2*sin |x + --|
      \    2 /
sin⁡(2x)2sin⁡2(x+π2)\frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x + \frac{\pi}{2} \right)}} 
    2     
 sec (x)  
----------
2*csc(2*x)
sec⁡2(x)2csc⁡(2x)\frac{\sec^{2}{\left(x \right)}}{2 \csc{\left(2 x \right)}} 
                2           
   /       2/x\\            
   |1 + tan |-|| *tan(x)    
   \        \2//            
----------------------------
                           2
/       2   \ /       2/x\\ 
\1 + tan (x)/*|1 - tan |-|| 
              \        \2//
(tan⁡2(x2)+1)2tan⁡(x)(1−tan⁡2(x2))2(tan⁡2(x)+1)\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \tan{\left(x \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(x \right)} + 1\right)} 
  1   
------
cot(x)
1cot⁡(x)\frac{1}{\cot{\left(x \right)}} 
   /      pi\
cos|2*x - --|
   \      2 /
-------------
       2     
  2*cos (x)
cos⁡(2x−π2)2cos⁡2(x)\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{2 \cos^{2}{\left(x \right)}} 
             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)}} 
  sin(2*x)  
------------
1 + cos(2*x)
sin⁡(2x)cos⁡(2x)+1\frac{\sin{\left(2 x \right)}}{\cos{\left(2 x \right)} + 1} 
             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)}} 
            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)} 
   2/pi    \
csc |-- - x|
    \2     /
------------
 2*csc(2*x)
csc⁡2(−x+π2)2csc⁡(2x)\frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{2 \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)}} 
   sec(x)  
-----------
   /    pi\
sec|x - --|
   \    2 /
sec⁡(x)sec⁡(x−π2)\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} 
sec(x)/sec(x - pi/2)
Potencias [src] 
   /   -2*I*x    2*I*x\ 
-I*\- e       + e     / 
------------------------
                   2    
     / I*x    -I*x\     
     |e      e    |     
   4*|---- + -----|     
     \ 2       2  /
−i(e2ix−e−2ix)4(eix2+e−ix2)2- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{4 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}} 
-i*(-exp(-2*i*x) + exp(2*i*x))/(4*(exp(i*x)/2 + exp(-i*x)/2)^2)
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