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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
                  2*sin(x)       
                  --------*cos(x)
    cos(2*x)         2           
--------------- - ---------------
cos(x) - sin(x)          2
−2sin⁡(x)2cos⁡(x)2+cos⁡(2x)−sin⁡(x)+cos⁡(x)- \frac{\frac{2 \sin{\left(x \right)}}{2} \cos{\left(x \right)}}{2} + \frac{\cos{\left(2 x \right)}}{- \sin{\left(x \right)} + \cos{\left(x \right)}} 
cos(2*x)/(cos(x) - sin(x)) - ((2*sin(x))/2)*cos(x)/2
Simplificación general [src] 
                    ___         
  cos(x)*sin(x)   \/ 2 *cos(2*x)
- ------------- + --------------
        2              /    pi\ 
                  2*cos|x + --| 
                       \    4 /
−sin⁡(x)cos⁡(x)2+2cos⁡(2x)2cos⁡(x+π4)- \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\sqrt{2} \cos{\left(2 x \right)}}{2 \cos{\left(x + \frac{\pi}{4} \right)}} 
-cos(x)*sin(x)/2 + sqrt(2)*cos(2*x)/(2*cos(x + pi/4))
Potencias [src] 
          -2*I*x    2*I*x             / I*x    -I*x\                 
         e         e                  |e      e    | /   -I*x    I*x\
         ------- + ------           I*|---- + -----|*\- e     + e   /
            2        2                \ 2       2  /                 
--------------------------------- + ---------------------------------
 I*x    -I*x     /   -I*x    I*x\                   4                
e      e       I*\- e     + e   /                                    
---- + ----- + ------------------                                    
 2       2             2
i(eix2+e−ix2)(eix−e−ix)4+e2ix2+e−2ix2i(eix−e−ix)2+eix2+e−ix2\frac{i \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right) \left(e^{i x} - e^{- i x}\right)}{4} + \frac{\frac{e^{2 i x}}{2} + \frac{e^{- 2 i x}}{2}}{\frac{i \left(e^{i x} - e^{- i x}\right)}{2} + \frac{e^{i x}}{2} + \frac{e^{- i x}}{2}} 
    cos(2*x)       cos(x)*sin(x)
---------------- - -------------
-sin(x) + cos(x)         2
−sin⁡(x)cos⁡(x)2+cos⁡(2x)−sin⁡(x)+cos⁡(x)- \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\cos{\left(2 x \right)}}{- \sin{\left(x \right)} + \cos{\left(x \right)}} 
cos(2*x)/(-sin(x) + cos(x)) - cos(x)*sin(x)/2
Denominador común [src] 
    cos(2*x)       cos(x)*sin(x)
---------------- - -------------
-sin(x) + cos(x)         2
−sin⁡(x)cos⁡(x)2+cos⁡(2x)−sin⁡(x)+cos⁡(x)- \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\cos{\left(2 x \right)}}{- \sin{\left(x \right)} + \cos{\left(x \right)}} 
cos(2*x)/(-sin(x) + cos(x)) - cos(x)*sin(x)/2
Denominador racional [src] 
4*cos(2*x) - 2*(-sin(x) + cos(x))*cos(x)*sin(x)
-----------------------------------------------
              -4*sin(x) + 4*cos(x)
−2(−sin⁡(x)+cos⁡(x))sin⁡(x)cos⁡(x)+4cos⁡(2x)−4sin⁡(x)+4cos⁡(x)\frac{- 2 \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)} + 4 \cos{\left(2 x \right)}}{- 4 \sin{\left(x \right)} + 4 \cos{\left(x \right)}} 
(4*cos(2*x) - 2*(-sin(x) + cos(x))*cos(x)*sin(x))/(-4*sin(x) + 4*cos(x))
Unión de expresiones racionales [src] 
2*cos(2*x) - (-sin(x) + cos(x))*cos(x)*sin(x)
---------------------------------------------
             2*(-sin(x) + cos(x))
−(−sin⁡(x)+cos⁡(x))sin⁡(x)cos⁡(x)+2cos⁡(2x)2(−sin⁡(x)+cos⁡(x))\frac{- \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)} + 2 \cos{\left(2 x \right)}}{2 \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)} 
(2*cos(2*x) - (-sin(x) + cos(x))*cos(x)*sin(x))/(2*(-sin(x) + cos(x)))
Compilar la expresión [src] 
    cos(2*x)       cos(x)*sin(x)
---------------- - -------------
-sin(x) + cos(x)         2
−sin⁡(x)cos⁡(x)2+cos⁡(2x)−sin⁡(x)+cos⁡(x)- \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\cos{\left(2 x \right)}}{- \sin{\left(x \right)} + \cos{\left(x \right)}} 
cos(2*x)/(-sin(x) + cos(x)) - cos(x)*sin(x)/2
Abrimos la expresión [src] 
                            2                      
         1             2*cos (x)      cos(x)*sin(x)
- --------------- + --------------- - -------------
  cos(x) - sin(x)   cos(x) - sin(x)         2
−sin⁡(x)cos⁡(x)2+2cos⁡2(x)−sin⁡(x)+cos⁡(x)−1−sin⁡(x)+cos⁡(x)- \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{2 \cos^{2}{\left(x \right)}}{- \sin{\left(x \right)} + \cos{\left(x \right)}} - \frac{1}{- \sin{\left(x \right)} + \cos{\left(x \right)}} 
-1/(cos(x) - sin(x)) + 2*cos(x)^2/(cos(x) - sin(x)) - cos(x)*sin(x)/2
Combinatoria [src] 
                2                2          
2*cos(2*x) + sin (x)*cos(x) - cos (x)*sin(x)
--------------------------------------------
            2*(-sin(x) + cos(x))
sin⁡2(x)cos⁡(x)−sin⁡(x)cos⁡2(x)+2cos⁡(2x)2(−sin⁡(x)+cos⁡(x))\frac{\sin^{2}{\left(x \right)} \cos{\left(x \right)} - \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 2 \cos{\left(2 x \right)}}{2 \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)} 
(2*cos(2*x) + sin(x)^2*cos(x) - cos(x)^2*sin(x))/(2*(-sin(x) + cos(x)))
Respuesta numérica [src] 
cos(2*x)/(-sin(x) + cos(x)) - 0.5*cos(x)*sin(x)
cos(2*x)/(-sin(x) + cos(x)) - 0.5*cos(x)*sin(x)
Parte trigonométrica [src] 
  sin(2*x)       ___    2/x   pi\    /x   pi\
- -------- + 2*\/ 2 *sin |- + --|*cot|- + --|
     4                   \2   8 /    \2   8 /
−sin⁡(2x)4+22sin⁡2(x2+π8)cot⁡(x2+π8)- \frac{\sin{\left(2 x \right)}}{4} + 2 \sqrt{2} \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} \cot{\left(\frac{x}{2} + \frac{\pi}{8} \right)} 
                        ___    /x   pi\
                    2*\/ 2 *tan|- + --|
       tan(x)                  \2   8 /
- --------------- + -------------------
    /       2   \            2/x   pi\ 
  2*\1 + tan (x)/     1 + tan |- + --| 
                              \2   8 /
22tan⁡(x2+π8)tan⁡2(x2+π8)+1−tan⁡(x)2(tan⁡2(x)+1)\frac{2 \sqrt{2} \tan{\left(\frac{x}{2} + \frac{\pi}{8} \right)}}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1} - \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} 
                      ___ /       2/x   pi\\ /        2   \
                    \/ 2 *|1 + cot |- + --||*\-1 + cot (x)/
       cot(x)             \        \2   8 //               
- --------------- + ---------------------------------------
    /       2   \       /       2   \ /        2/x   pi\\  
  2*\1 + cot (x)/     2*\1 + cot (x)/*|-1 + cot |- + --||  
                                      \         \2   8 //
2(cot⁡2(x)−1)(cot⁡2(x2+π8)+1)2(cot⁡2(x)+1)(cot⁡2(x2+π8)−1)−cot⁡(x)2(cot⁡2(x)+1)\frac{\sqrt{2} \left(\cot^{2}{\left(x \right)} - 1\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right)}{2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} - 1\right)} - \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)} 
                 ___    /x   pi\
             2*\/ 2 *tan|- + --|
  sin(2*x)              \2   8 /
- -------- + -------------------
     4                2/x   pi\ 
               1 + tan |- + --| 
                       \2   8 /
−sin⁡(2x)4+22tan⁡(x2+π8)tan⁡2(x2+π8)+1- \frac{\sin{\left(2 x \right)}}{4} + \frac{2 \sqrt{2} \tan{\left(\frac{x}{2} + \frac{\pi}{8} \right)}}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1} 
               ___             /    pi\
             \/ 2 *cos(2*x)*sec|x + --|
  sin(2*x)                     \    4 /
- -------- + --------------------------
     4                   2
−sin⁡(2x)4+2cos⁡(2x)sec⁡(x+π4)2- \frac{\sin{\left(2 x \right)}}{4} + \frac{\sqrt{2} \cos{\left(2 x \right)} \sec{\left(x + \frac{\pi}{4} \right)}}{2} 
                 ___    /     pi\
               \/ 2 *csc|-x + --|
      1                 \     4 /
- ---------- + ------------------
  4*csc(2*x)         /pi      \  
                2*csc|-- - 2*x|  
                     \2       /
2csc⁡(−x+π4)2csc⁡(−2x+π2)−14csc⁡(2x)\frac{\sqrt{2} \csc{\left(- x + \frac{\pi}{4} \right)}}{2 \csc{\left(- 2 x + \frac{\pi}{2} \right)}} - \frac{1}{4 \csc{\left(2 x \right)}} 
  sin(2*x)     ___    /    pi\
- -------- + \/ 2 *cos|x - --|
     4                \    4 /
−sin⁡(2x)4+2cos⁡(x−π4)- \frac{\sin{\left(2 x \right)}}{4} + \sqrt{2} \cos{\left(x - \frac{\pi}{4} \right)} 
                      ___ /       2/x   pi\\ /       2   \
                    \/ 2 *|1 + tan |- + --||*\1 - tan (x)/
       tan(x)             \        \2   8 //              
- --------------- + --------------------------------------
    /       2   \       /       2   \ /       2/x   pi\\  
  2*\1 + tan (x)/     2*\1 + tan (x)/*|1 - tan |- + --||  
                                      \        \2   8 //
2(1−tan⁡2(x))(tan⁡2(x2+π8)+1)2(1−tan⁡2(x2+π8))(tan⁡2(x)+1)−tan⁡(x)2(tan⁡2(x)+1)\frac{\sqrt{2} \left(1 - \tan^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} - \frac{\tan{\left(x \right)}}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} 
                                   /    pi\
                         cos(x)*cos|x - --|
       cos(2*x)                    \    2 /
---------------------- - ------------------
     /    pi\                    2         
- cos|x - --| + cos(x)                     
     \    2 /
−cos⁡(x)cos⁡(x−π2)2+cos⁡(2x)cos⁡(x)−cos⁡(x−π2)- \frac{\cos{\left(x \right)} \cos{\left(x - \frac{\pi}{2} \right)}}{2} + \frac{\cos{\left(2 x \right)}}{\cos{\left(x \right)} - \cos{\left(x - \frac{\pi}{2} \right)}} 
                                             /        2/x\\    /x\
                       2                     |-1 + cot |-||*cot|-|
               -1 + cot (x)                  \         \2//    \2/
------------------------------------------ - ---------------------
              /        2/x\          /x\ \                    2   
              |-1 + cot |-|     2*cot|-| |       /       2/x\\    
/       2   \ |         \2/          \2/ |       |1 + cot |-||    
\1 + cot (x)/*|------------ - -----------|       \        \2//    
              |       2/x\           2/x\|                        
              |1 + cot |-|    1 + cot |-||                        
              \        \2/            \2//
−(cot⁡2(x2)−1)cot⁡(x2)(cot⁡2(x2)+1)2+cot⁡2(x)−1(cot⁡2(x2)−1cot⁡2(x2)+1−2cot⁡(x2)cot⁡2(x2)+1)(cot⁡2(x)+1)- \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \cot{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} + \frac{\cot^{2}{\left(x \right)} - 1}{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)} 
       /pi      \                 /    pi\
    sin|-- + 2*x|       sin(x)*sin|x + --|
       \2       /                 \    2 /
--------------------- - ------------------
             /    pi\           2         
-sin(x) + sin|x + --|                     
             \    2 /
−sin⁡(x)sin⁡(x+π2)2+sin⁡(2x+π2)−sin⁡(x)+sin⁡(x+π2)- \frac{\sin{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{2} + \frac{\sin{\left(2 x + \frac{\pi}{2} \right)}}{- \sin{\left(x \right)} + \sin{\left(x + \frac{\pi}{2} \right)}} 
               ___             /     pi\
             \/ 2 *cos(2*x)*csc|-x + --|
  sin(2*x)                     \     4 /
- -------- + ---------------------------
     4                    2
−sin⁡(2x)4+2cos⁡(2x)csc⁡(−x+π4)2- \frac{\sin{\left(2 x \right)}}{4} + \frac{\sqrt{2} \cos{\left(2 x \right)} \csc{\left(- x + \frac{\pi}{4} \right)}}{2} 
                         ___   
         1             \/ 2    
- --------------- + -----------
       /      pi\      /    pi\
  4*sec|2*x - --|   sec|x - --|
       \      2 /      \    4 /
−14sec⁡(2x−π2)+2sec⁡(x−π4)- \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{\sqrt{2}}{\sec{\left(x - \frac{\pi}{4} \right)}} 
                      ___    /    pi\
                    \/ 2 *sec|x + --|
         1                   \    4 /
- --------------- + -----------------
       /      pi\       2*sec(2*x)   
  4*sec|2*x - --|                    
       \      2 /
−14sec⁡(2x−π2)+2sec⁡(x+π4)2sec⁡(2x)- \frac{1}{4 \sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{\sqrt{2} \sec{\left(x + \frac{\pi}{4} \right)}}{2 \sec{\left(2 x \right)}} 
            1                       1       
-------------------------- - ---------------
/  1        1   \            2*csc(x)*sec(x)
|------ - ------|*sec(2*x)                  
\sec(x)   csc(x)/
−12csc⁡(x)sec⁡(x)+1(1sec⁡(x)−1csc⁡(x))sec⁡(2x)- \frac{1}{2 \csc{\left(x \right)} \sec{\left(x \right)}} + \frac{1}{\left(\frac{1}{\sec{\left(x \right)}} - \frac{1}{\csc{\left(x \right)}}\right) \sec{\left(2 x \right)}} 
               ___         
  sin(2*x)   \/ 2 *cos(2*x)
- -------- + --------------
     4            /    pi\ 
             2*cos|x + --| 
                  \    4 /
−sin⁡(2x)4+2cos⁡(2x)2cos⁡(x+π4)- \frac{\sin{\left(2 x \right)}}{4} + \frac{\sqrt{2} \cos{\left(2 x \right)}}{2 \cos{\left(x + \frac{\pi}{4} \right)}} 
               1                           1          
------------------------------- - --------------------
/  1           1     \                        /    pi\
|------ - -----------|*sec(2*x)   2*sec(x)*sec|x - --|
|sec(x)      /    pi\|                        \    2 /
|         sec|x - --||                                
\            \    2 //
−12sec⁡(x)sec⁡(x−π2)+1(−1sec⁡(x−π2)+1sec⁡(x))sec⁡(2x)- \frac{1}{2 \sec{\left(x \right)} \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\left(- \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}\right) \sec{\left(2 x \right)}} 
  sin(2*x)     ___    /    pi\
- -------- + \/ 2 *sin|x + --|
     4                \    4 /
−sin⁡(2x)4+2sin⁡(x+π4)- \frac{\sin{\left(2 x \right)}}{4} + \sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)} 
               ___    /pi      \
             \/ 2 *sin|-- + 2*x|
  sin(2*x)            \2       /
- -------- + -------------------
     4              /    3*pi\  
               2*sin|x + ----|  
                    \     4  /
−sin⁡(2x)4+2sin⁡(2x+π2)2sin⁡(x+3π4)- \frac{\sin{\left(2 x \right)}}{4} + \frac{\sqrt{2} \sin{\left(2 x + \frac{\pi}{2} \right)}}{2 \sin{\left(x + \frac{3 \pi}{4} \right)}} 
               ___    2    /       2/x   pi\\ /       2   \
             \/ 2 *cos (x)*|1 + tan |- + --||*\1 - tan (x)/
  sin(2*x)                 \        \2   8 //              
- -------- + ----------------------------------------------
     4                      /       2/x   pi\\             
                          2*|1 - tan |- + --||             
                            \        \2   8 //
2(1−tan⁡2(x))(tan⁡2(x2+π8)+1)cos⁡2(x)2(1−tan⁡2(x2+π8))−sin⁡(2x)4\frac{\sqrt{2} \left(1 - \tan^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(x \right)}}{2 \left(1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)}\right)} - \frac{\sin{\left(2 x \right)}}{4} 
                    ___   
      1           \/ 2    
- ---------- + -----------
  4*csc(2*x)      /    pi\
               csc|x + --|
                  \    4 /
2csc⁡(x+π4)−14csc⁡(2x)\frac{\sqrt{2}}{\csc{\left(x + \frac{\pi}{4} \right)}} - \frac{1}{4 \csc{\left(2 x \right)}} 
                        ___    /x   pi\
                    2*\/ 2 *cot|- + --|
       cot(x)                  \2   8 /
- --------------- + -------------------
    /       2   \            2/x   pi\ 
  2*\1 + cot (x)/     1 + cot |- + --| 
                              \2   8 /
22cot⁡(x2+π8)cot⁡2(x2+π8)+1−cot⁡(x)2(cot⁡2(x)+1)\frac{2 \sqrt{2} \cot{\left(\frac{x}{2} + \frac{\pi}{8} \right)}}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{8} \right)} + 1} - \frac{\cot{\left(x \right)}}{2 \left(\cot^{2}{\left(x \right)} + 1\right)} 
                                   ___                            
  sin(2*x)                       \/ 2 *cos(2*x)                   
- -------- - -----------------------------------------------------
     4                           ___________    ___________       
                 ___            /       ___    /       ___        
             - \/ 2 *cos(x) + \/  2 + \/ 2  *\/  2 - \/ 2  *sin(x)
−sin⁡(2x)4−2cos⁡(2x)2−22+2sin⁡(x)−2cos⁡(x)- \frac{\sin{\left(2 x \right)}}{4} - \frac{\sqrt{2} \cos{\left(2 x \right)}}{\sqrt{2 - \sqrt{2}} \sqrt{\sqrt{2} + 2} \sin{\left(x \right)} - \sqrt{2} \cos{\left(x \right)}} 
                                            /       2/x\\    /x\
                      2                     |1 - tan |-||*tan|-|
               1 - tan (x)                  \        \2//    \2/
----------------------------------------- - --------------------
              /       2/x\          /x\ \                   2   
              |1 - tan |-|     2*tan|-| |      /       2/x\\    
/       2   \ |        \2/          \2/ |      |1 + tan |-||    
\1 + tan (x)/*|----------- - -----------|      \        \2//    
              |       2/x\          2/x\|                       
              |1 + tan |-|   1 + tan |-||                       
              \        \2/           \2//
−(1−tan⁡2(x2))tan⁡(x2)(tan⁡2(x2)+1)2+1−tan⁡2(x)(1−tan⁡2(x2)tan⁡2(x2)+1−2tan⁡(x2)tan⁡2(x2)+1)(tan⁡2(x)+1)- \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \tan{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} + \frac{1 - \tan^{2}{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)} 
     /      pi\                    
  cos|2*x - --|                    
     \      2 /     ___    /    pi\
- ------------- + \/ 2 *cos|x - --|
        4                  \    4 /
2cos⁡(x−π4)−cos⁡(2x−π2)4\sqrt{2} \cos{\left(x - \frac{\pi}{4} \right)} - \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} 
     /      pi\                 
  cos|2*x - --|     ___         
     \      2 /   \/ 2 *cos(2*x)
- ------------- + --------------
        4              /    pi\ 
                  2*cos|x + --| 
                       \    4 /
2cos⁡(2x)2cos⁡(x+π4)−cos⁡(2x−π2)4\frac{\sqrt{2} \cos{\left(2 x \right)}}{2 \cos{\left(x + \frac{\pi}{4} \right)}} - \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{4} 
                 1                              1          
------------------------------------ - --------------------
/     1          1   \    /pi      \               /pi    \
|----------- - ------|*csc|-- - 2*x|   2*csc(x)*csc|-- - x|
|   /pi    \   csc(x)|    \2       /               \2     /
|csc|-- - x|         |                                     
\   \2     /         /
−12csc⁡(x)csc⁡(−x+π2)+1(1csc⁡(−x+π2)−1csc⁡(x))csc⁡(−2x+π2)- \frac{1}{2 \csc{\left(x \right)} \csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(x \right)}}\right) \csc{\left(- 2 x + \frac{\pi}{2} \right)}} 
    cos(2*x)       cos(x)*sin(x)
---------------- - -------------
-sin(x) + cos(x)         2
−sin⁡(x)cos⁡(x)2+cos⁡(2x)−sin⁡(x)+cos⁡(x)- \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\cos{\left(2 x \right)}}{- \sin{\left(x \right)} + \cos{\left(x \right)}} 
cos(2*x)/(-sin(x) + cos(x)) - cos(x)*sin(x)/2
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