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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
    cos(2*x)   
---------------
sin(2*x)*cos(x)
cos⁡(2x)sin⁡(2x)cos⁡(x)\frac{\cos{\left(2 x \right)}}{\sin{\left(2 x \right)} \cos{\left(x \right)}} 
cos(2*x)/((sin(2*x)*cos(x)))
Simplificación general [src] 
       1       
---------------
cos(x)*tan(2*x)
1cos⁡(x)tan⁡(2x)\frac{1}{\cos{\left(x \right)} \tan{\left(2 x \right)}} 
1/(cos(x)*tan(2*x))
Abrimos la expresión [src] 
  1             1        
------ - ----------------
sin(x)        2          
         2*cos (x)*sin(x)
1sin⁡(x)−12sin⁡(x)cos⁡2(x)\frac{1}{\sin{\left(x \right)}} - \frac{1}{2 \sin{\left(x \right)} \cos^{2}{\left(x \right)}} 
1/sin(x) - 1/(2*cos(x)^2*sin(x))
Respuesta numérica [src] 
cos(2*x)/(cos(x)*sin(2*x))
cos(2*x)/(cos(x)*sin(2*x))
Potencias [src] 
           / -2*I*x    2*I*x\      
           |e         e     |      
       2*I*|------- + ------|      
           \   2        2   /      
-----------------------------------
/ I*x    -I*x\                     
|e      e    | /   -2*I*x    2*I*x\
|---- + -----|*\- e       + e     /
\ 2       2  /
2i(e2ix2+e−2ix2)(eix2+e−ix2)(e2ix−e−2ix)\frac{2 i \left(\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}\right)}{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(e^{2 i x} - e^{- 2 i x}\right)} 
2*i*(exp(-2*i*x)/2 + exp(2*i*x)/2)/((exp(i*x)/2 + exp(-i*x)/2)*(-exp(-2*i*x) + exp(2*i*x)))
Parte trigonométrica [src] 
 /    1            \ 
-|- ------ + tan(x)| 
 \  tan(x)         / 
---------------------
       2*cos(x)
−tan⁡(x)−1tan⁡(x)2cos⁡(x)- \frac{\tan{\left(x \right)} - \frac{1}{\tan{\left(x \right)}}}{2 \cos{\left(x \right)}} 
/       2/x\\ /        2   \
|1 + cot |-||*\-1 + cot (x)/
\        \2//               
----------------------------
    /        2/x\\          
  2*|-1 + cot |-||*cot(x)   
    \         \2//
(cot⁡2(x2)+1)(cot⁡2(x)−1)2(cot⁡2(x2)−1)cot⁡(x)\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(x \right)} - 1\right)}{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \cot{\left(x \right)}} 
/       2/x\\         
|1 + cot |-||*cot(2*x)
\        \2//         
----------------------
             2/x\     
     -1 + cot |-|     
              \2/
(cot⁡2(x2)+1)cot⁡(2x)cot⁡2(x2)−1\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(2 x \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} - 1} 
csc(2*x)*sec(x)
---------------
    sec(2*x)
csc⁡(2x)sec⁡(x)sec⁡(2x)\frac{\csc{\left(2 x \right)} \sec{\left(x \right)}}{\sec{\left(2 x \right)}} 
             1                        
           ------ - cot(x)            
           cot(x)                     
--------------------------------------
  /                2                 \
  |  /        2/x\\           2/x\   |
  |  |-1 + cot |-||      4*cot |-|   |
  |  \         \4//            \4/   |
2*|- --------------- + --------------|
  |                2                2|
  |   /       2/x\\    /       2/x\\ |
  |   |1 + cot |-||    |1 + cot |-|| |
  \   \        \4//    \        \4// /
−cot⁡(x)+1cot⁡(x)2(−(cot⁡2(x4)−1)2(cot⁡2(x4)+1)2+4cot⁡2(x4)(cot⁡2(x4)+1)2)\frac{- \cot{\left(x \right)} + \frac{1}{\cot{\left(x \right)}}}{2 \left(- \frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} + \frac{4 \cot^{2}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}\right)} 
      cos(2*x)      
--------------------
          /      pi\
cos(x)*cos|2*x - --|
          \      2 /
cos⁡(2x)cos⁡(x)cos⁡(2x−π2)\frac{\cos{\left(2 x \right)}}{\cos{\left(x \right)} \cos{\left(2 x - \frac{\pi}{2} \right)}} 
        sin(4*x)       
-----------------------
     2         /    pi\
2*sin (2*x)*sin|x + --|
               \    2 /
sin⁡(4x)2sin⁡2(2x)sin⁡(x+π2)\frac{\sin{\left(4 x \right)}}{2 \sin^{2}{\left(2 x \right)} \sin{\left(x + \frac{\pi}{2} \right)}} 
                 /    pi\ 
              sec|x - --| 
   sec(x)        \    2 / 
----------- - ----------- 
   /    pi\      sec(x)   
sec|x - --|               
   \    2 /               
--------------------------
  /     1            1   \
2*|------------ - -------|
  |   2/x   pi\      2/x\|
  |sec |- - --|   sec |-||
  \    \2   2 /       \2//
sec⁡(x)sec⁡(x−π2)−sec⁡(x−π2)sec⁡(x)2(1sec⁡2(x2−π2)−1sec⁡2(x2))\frac{\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} - \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}}{2 \left(\frac{1}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{1}{\sec^{2}{\left(\frac{x}{2} \right)}}\right)} 
   /    pi\               
cos|x - --|               
   \    2 /      cos(x)   
----------- - ----------- 
   cos(x)        /    pi\ 
              cos|x - --| 
                 \    2 / 
--------------------------
  /   2/x   pi\      2/x\\
2*|cos |- - --| - cos |-||
  \    \2   2 /       \2//
−cos⁡(x)cos⁡(x−π2)+cos⁡(x−π2)cos⁡(x)2(−cos⁡2(x2)+cos⁡2(x2−π2))\frac{- \frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}}{2 \left(- \cos^{2}{\left(\frac{x}{2} \right)} + \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}\right)} 
            2/x\      
     1 + tan |-|      
             \2/      
----------------------
/       2/x\\         
|1 - tan |-||*tan(2*x)
\        \2//
tan⁡2(x2)+1(1−tan⁡2(x2))tan⁡(2x)\frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(2 x \right)}} 
       2                  
  2*sin (x)    sin(2*x)   
  --------- - ---------   
   sin(2*x)        2      
              2*sin (x)   
--------------------------
  /   2/x\      2/pi   x\\
2*|sin |-| - sin |-- + -||
  \    \2/       \2    2//
2sin⁡2(x)sin⁡(2x)−sin⁡(2x)2sin⁡2(x)2(sin⁡2(x2)−sin⁡2(x2+π2))\frac{\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} - \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}}{2 \left(\sin^{2}{\left(\frac{x}{2} \right)} - \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}\right)} 
-(-cot(x) + tan(x)) 
--------------------
      2*cos(x)
−tan⁡(x)−cot⁡(x)2cos⁡(x)- \frac{\tan{\left(x \right)} - \cot{\left(x \right)}}{2 \cos{\left(x \right)}} 
       1       
---------------
cos(x)*tan(2*x)
1cos⁡(x)tan⁡(2x)\frac{1}{\cos{\left(x \right)} \tan{\left(2 x \right)}} 
   /pi    \               
csc|-- - x|               
   \2     /      csc(x)   
----------- - ----------- 
   csc(x)        /pi    \ 
              csc|-- - x| 
                 \2     / 
--------------------------
  /   1           1      \
2*|------- - ------------|
  |   2/x\      2/pi   x\|
  |csc |-|   csc |-- - -||
  \    \2/       \2    2//
−csc⁡(x)csc⁡(−x+π2)+csc⁡(−x+π2)csc⁡(x)2(−1csc⁡2(−x2+π2)+1csc⁡2(x2))\frac{- \frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}}{2 \left(- \frac{1}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)} 
     sin(4*x)     
------------------
            2     
2*cos(x)*sin (2*x)
sin⁡(4x)2sin⁡2(2x)cos⁡(x)\frac{\sin{\left(4 x \right)}}{2 \sin^{2}{\left(2 x \right)} \cos{\left(x \right)}} 
            /pi    \
csc(2*x)*csc|-- - x|
            \2     /
--------------------
      /pi      \    
   csc|-- - 2*x|    
      \2       /
csc⁡(2x)csc⁡(−x+π2)csc⁡(−2x+π2)\frac{\csc{\left(2 x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}} 
      /pi      \    
   sin|-- + 2*x|    
      \2       /    
--------------------
            /    pi\
sin(2*x)*sin|x + --|
            \    2 /
sin⁡(2x+π2)sin⁡(2x)sin⁡(x+π2)\frac{\sin{\left(2 x + \frac{\pi}{2} \right)}}{\sin{\left(2 x \right)} \sin{\left(x + \frac{\pi}{2} \right)}} 
              1                      
          - ------ + tan(x)          
            tan(x)                   
-------------------------------------
  /               2                 \
  |  /       2/x\\           2/x\   |
  |  |1 - tan |-||      4*tan |-|   |
  |  \        \4//            \4/   |
2*|- -------------- + --------------|
  |               2                2|
  |  /       2/x\\    /       2/x\\ |
  |  |1 + tan |-||    |1 + tan |-|| |
  \  \        \4//    \        \4// /
tan⁡(x)−1tan⁡(x)2(−(1−tan⁡2(x4))2(tan⁡2(x4)+1)2+4tan⁡2(x4)(tan⁡2(x4)+1)2)\frac{\tan{\left(x \right)} - \frac{1}{\tan{\left(x \right)}}}{2 \left(- \frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{x}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}\right)} 
/       2/x\\ /       2   \
|1 + tan |-||*\1 - tan (x)/
\        \2//              
---------------------------
     /       2/x\\         
   2*|1 - tan |-||*tan(x)  
     \        \2//
(1−tan⁡2(x))(tan⁡2(x2)+1)2(1−tan⁡2(x2))tan⁡(x)\frac{\left(1 - \tan^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(x \right)}} 
      1              
  - ------ + tan(x)  
    tan(x)           
---------------------
  /   2/x\      2/x\\
2*|sin |-| - cos |-||
  \    \2/       \2//
tan⁡(x)−1tan⁡(x)2(sin⁡2(x2)−cos⁡2(x2))\frac{\tan{\left(x \right)} - \frac{1}{\tan{\left(x \right)}}}{2 \left(\sin^{2}{\left(\frac{x}{2} \right)} - \cos^{2}{\left(\frac{x}{2} \right)}\right)} 
    2*cos(2*x)   
-----------------
sin(x) + sin(3*x)
2cos⁡(2x)sin⁡(x)+sin⁡(3x)\frac{2 \cos{\left(2 x \right)}}{\sin{\left(x \right)} + \sin{\left(3 x \right)}} 
          /      pi\
sec(x)*sec|2*x - --|
          \      2 /
--------------------
      sec(2*x)
sec⁡(x)sec⁡(2x−π2)sec⁡(2x)\frac{\sec{\left(x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sec{\left(2 x \right)}} 
sec(x)*sec(2*x - pi/2)/sec(2*x)
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