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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   sin(x)                
------------*(1 + sin(x))
/       /x\\             
|1 - tan|-||             
|       \2/|             
|----------|             
|       /x\|             
|1 + tan|-||             
\       \2//
sin⁡(x)(1−tan⁡(x2))1tan⁡(x2)+1(sin⁡(x)+1)\frac{\sin{\left(x \right)}}{\left(1 - \tan{\left(\frac{x}{2} \right)}\right) \frac{1}{\tan{\left(\frac{x}{2} \right)} + 1}} \left(\sin{\left(x \right)} + 1\right) 
(sin(x)/(((1 - tan(x/2))/(1 + tan(x/2)))))*(1 + sin(x))
Simplificación general [src] 
              /       /x\\        
-(1 + sin(x))*|1 + tan|-||*sin(x) 
              \       \2//        
----------------------------------
                   /x\            
           -1 + tan|-|            
                   \2/
−(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x)tan⁡(x2)−1- \frac{\left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(\frac{x}{2} \right)} - 1} 
-(1 + sin(x))*(1 + tan(x/2))*sin(x)/(-1 + tan(x/2))
Respuesta numérica [src] 
(1.0 + sin(x))*(1.0 + tan(x/2))*sin(x)/(1.0 - tan(x/2))
(1.0 + sin(x))*(1.0 + tan(x/2))*sin(x)/(1.0 - tan(x/2))
Denominador racional [src] 
             /       /x\\       
(1 + sin(x))*|1 + tan|-||*sin(x)
             \       \2//       
--------------------------------
                  /x\           
           1 - tan|-|           
                  \2/
(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x)1−tan⁡(x2)\frac{\left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(x \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
(1 + sin(x))*(1 + tan(x/2))*sin(x)/(1 - tan(x/2))
Denominador común [src] 
                          2              
     2               2*sin (x) + 2*sin(x)
- sin (x) - sin(x) - --------------------
                                 /x\     
                         -1 + tan|-|     
                                 \2/
−2sin⁡2(x)+2sin⁡(x)tan⁡(x2)−1−sin⁡2(x)−sin⁡(x)- \frac{2 \sin^{2}{\left(x \right)} + 2 \sin{\left(x \right)}}{\tan{\left(\frac{x}{2} \right)} - 1} - \sin^{2}{\left(x \right)} - \sin{\left(x \right)} 
-sin(x)^2 - sin(x) - (2*sin(x)^2 + 2*sin(x))/(-1 + tan(x/2))
Potencias [src] 
             /       /x\\       
(1 + sin(x))*|1 + tan|-||*sin(x)
             \       \2//       
--------------------------------
                  /x\           
           1 - tan|-|           
                  \2/
(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x)1−tan⁡(x2)\frac{\left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(x \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
                            /      /   I*x    -I*x \\                  
                            |      |   ---    -----||                  
   /      /   -I*x    I*x\\ |      |    2       2  ||                  
   |    I*\- e     + e   /| |    I*\- e    + e     /| /   -I*x    I*x\ 
-I*|1 - ------------------|*|1 + -------------------|*\- e     + e   / 
   \            2         / |        I*x    -I*x    |                  
                            |        ---    -----   |                  
                            |         2       2     |                  
                            \       e    + e        /                  
-----------------------------------------------------------------------
                        /      /   I*x    -I*x \\                      
                        |      |   ---    -----||                      
                        |      |    2       2  ||                      
                        |    I*\- e    + e     /|                      
                      2*|1 - -------------------|                      
                        |        I*x    -I*x    |                      
                        |        ---    -----   |                      
                        |         2       2     |                      
                        \       e    + e        /
−i(−i(eix−e−ix)2+1)(i(−eix2+e−ix2)eix2+e−ix2+1)(eix−e−ix)2(−i(−eix2+e−ix2)eix2+e−ix2+1)- \frac{i \left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1\right) \left(\frac{i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} + 1\right) \left(e^{i x} - e^{- i x}\right)}{2 \left(- \frac{i \left(- e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}\right)}{e^{\frac{i x}{2}} + e^{- \frac{i x}{2}}} + 1\right)} 
-i*(1 - i*(-exp(-i*x) + exp(i*x))/2)*(1 + i*(-exp(i*x/2) + exp(-i*x/2))/(exp(i*x/2) + exp(-i*x/2)))*(-exp(-i*x) + exp(i*x))/(2*(1 - i*(-exp(i*x/2) + exp(-i*x/2))/(exp(i*x/2) + exp(-i*x/2))))
Unión de expresiones racionales [src] 
             /       /x\\       
(1 + sin(x))*|1 + tan|-||*sin(x)
             \       \2//       
--------------------------------
                  /x\           
           1 - tan|-|           
                  \2/
(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x)1−tan⁡(x2)\frac{\left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(x \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
(1 + sin(x))*(1 + tan(x/2))*sin(x)/(1 - tan(x/2))
Combinatoria [src] 
              /       /x\\        
-(1 + sin(x))*|1 + tan|-||*sin(x) 
              \       \2//        
----------------------------------
                   /x\            
           -1 + tan|-|            
                   \2/
−(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x)tan⁡(x2)−1- \frac{\left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(\frac{x}{2} \right)} - 1} 
-(1 + sin(x))*(1 + tan(x/2))*sin(x)/(-1 + tan(x/2))
Compilar la expresión [src] 
             /       /x\\       
(1 + sin(x))*|1 + tan|-||*sin(x)
             \       \2//       
--------------------------------
                  /x\           
           1 - tan|-|           
                  \2/
(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x)1−tan⁡(x2)\frac{\left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(x \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
(1 + sin(x))*(1 + tan(x/2))*sin(x)/(1 - tan(x/2))
Parte trigonométrica [src] 
                 /           /x\ \                    
               2 |      2*tan|-| |                    
  /       2/x\\  |           \2/ | /       /x\\    /x\
2*|1 - tan |-|| *|1 + -----------|*|1 + tan|-||*tan|-|
  \        \4//  |           2/x\| \       \2//    \2/
                 |    1 + tan |-||                    
                 \            \2//                    
------------------------------------------------------
                          2                           
             /       2/x\\  /       /x\\              
             |1 + tan |-|| *|1 - tan|-||              
             \        \4//  \       \2//
2(1+2tan⁡(x2)tan⁡2(x2)+1)(1−tan⁡2(x4))2(tan⁡(x2)+1)tan⁡(x2)(1−tan⁡(x2))(tan⁡2(x4)+1)2\frac{2 \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}{\left(1 - \tan{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} 
  /       /x   pi\\                                     
  |    cos|- - --||                                     
  |       \2   2 /| /       /    pi\\    /x\    /x   pi\
2*|1 + -----------|*|1 + cos|x - --||*cos|-|*cos|- - --|
  |          /x\  | \       \    2 //    \2/    \2   2 /
  |       cos|-|  |                                     
  \          \2/  /                                     
--------------------------------------------------------
                           /x   pi\                     
                        cos|- - --|                     
                           \2   2 /                     
                    1 - -----------                     
                              /x\                       
                           cos|-|                       
                              \2/
2(1+cos⁡(x2−π2)cos⁡(x2))(cos⁡(x−π2)+1)cos⁡(x2)cos⁡(x2−π2)1−cos⁡(x2−π2)cos⁡(x2)\frac{2 \left(1 + \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}}\right) \left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{1 - \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}}} 
     2/x\              /       /x\\    /x\
2*cos |-|*(1 + sin(x))*|1 + tan|-||*tan|-|
      \2/              \       \2//    \2/
------------------------------------------
                       /x\                
                1 - tan|-|                
                       \2/
2(sin⁡(x)+1)(tan⁡(x2)+1)cos⁡2(x2)tan⁡(x2)1−tan⁡(x2)\frac{2 \left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
                       /         2/x\\             
                       |    2*sin |-||             
     2/x\    2/pi   x\ |          \2/|             
4*sin |-|*sin |-- + -|*|1 + ---------|*(1 + sin(x))
      \2/     \2    2/ \      sin(x) /             
---------------------------------------------------
               /         2/x\\                     
               |    2*sin |-||                     
               |          \2/|                     
               |1 - ---------|*sin(x)              
               \      sin(x) /
4(2sin⁡2(x2)sin⁡(x)+1)(sin⁡(x)+1)sin⁡2(x2)sin⁡2(x2+π2)(−2sin⁡2(x2)sin⁡(x)+1)sin⁡(x)\frac{4 \left(\frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + 1\right) \left(\sin{\left(x \right)} + 1\right) \sin^{2}{\left(\frac{x}{2} \right)} \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{\left(- \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + 1\right) \sin{\left(x \right)}} 
             /       /pi   x\\
             |    csc|-- - -||
/      1   \ |       \2    2/|
|1 + ------|*|1 + -----------|
\    csc(x)/ |          /x\  |
             |       csc|-|  |
             \          \2/  /
------------------------------
   /       /pi   x\\          
   |    csc|-- - -||          
   |       \2    2/|          
   |1 - -----------|*csc(x)   
   |          /x\  |          
   |       csc|-|  |          
   \          \2/  /
(1+csc⁡(−x2+π2)csc⁡(x2))(1+1csc⁡(x))(1−csc⁡(−x2+π2)csc⁡(x2))csc⁡(x)\frac{\left(1 + \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right) \left(1 + \frac{1}{\csc{\left(x \right)}}\right)}{\left(1 - \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right) \csc{\left(x \right)}} 
  /           /x\ \ /                    2/x\\       
  |      2*tan|-| | |             1 + tan |-||       
  |           \2/ | |      1              \2/|    /x\
2*|1 + -----------|*|1 - ------ + -----------|*tan|-|
  |           2/x\| |    tan(x)          /x\ |    \2/
  |    1 + tan |-|| |               2*tan|-| |       
  \            \2// \                    \2/ /       
-----------------------------------------------------
                     /                    2/x\\      
                     |             1 + tan |-||      
       /       2/x\\ |      1              \2/|      
       |1 + tan |-||*|1 + ------ - -----------|      
       \        \2// |    tan(x)          /x\ |      
                     |               2*tan|-| |      
                     \                    \2/ /
2(1+2tan⁡(x2)tan⁡2(x2)+1)(tan⁡2(x2)+12tan⁡(x2)+1−1tan⁡(x))tan⁡(x2)(tan⁡2(x2)+1)(−tan⁡2(x2)+12tan⁡(x2)+1+1tan⁡(x))\frac{2 \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{2 \tan{\left(\frac{x}{2} \right)}} + 1 - \frac{1}{\tan{\left(x \right)}}\right) \tan{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(- \frac{\tan^{2}{\left(\frac{x}{2} \right)} + 1}{2 \tan{\left(\frac{x}{2} \right)}} + 1 + \frac{1}{\tan{\left(x \right)}}\right)} 
     2/x\              /      1        1   \    /x\
2*cos |-|*(1 + sin(x))*|1 + ------ - ------|*tan|-|
      \2/              \    sin(x)   tan(x)/    \2/
---------------------------------------------------
                      1        1                   
                1 + ------ - ------                
                    tan(x)   sin(x)
2(sin⁡(x)+1)(1−1tan⁡(x)+1sin⁡(x))cos⁡2(x2)tan⁡(x2)1+1tan⁡(x)−1sin⁡(x)\frac{2 \left(\sin{\left(x \right)} + 1\right) \left(1 - \frac{1}{\tan{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right) \cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}}{1 + \frac{1}{\tan{\left(x \right)}} - \frac{1}{\sin{\left(x \right)}}} 
             /       /x\\       
(1 + sin(x))*|1 + tan|-||*sin(x)
             \       \2//       
--------------------------------
                  /x\           
           1 - tan|-|           
                  \2/
(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x)1−tan⁡(x2)\frac{\left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(x \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
/       /x   pi\\                              
|    cos|- - --||                              
|       \2   2 /| /       /    pi\\    /    pi\
|1 + -----------|*|1 + cos|x - --||*cos|x - --|
|          /x\  | \       \    2 //    \    2 /
|       cos|-|  |                              
\          \2/  /                              
-----------------------------------------------
                       /x   pi\                
                    cos|- - --|                
                       \2   2 /                
                1 - -----------                
                          /x\                  
                       cos|-|                  
                          \2/
(1+cos⁡(x2−π2)cos⁡(x2))(cos⁡(x−π2)+1)cos⁡(x−π2)1−cos⁡(x2−π2)cos⁡(x2)\frac{\left(1 + \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}}\right) \left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right) \cos{\left(x - \frac{\pi}{2} \right)}}{1 - \frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}}} 
             /      1        1   \       
(1 + sin(x))*|1 + ------ - ------|*sin(x)
             \    sin(x)   tan(x)/       
-----------------------------------------
                 1        1              
           1 + ------ - ------           
               tan(x)   sin(x)
(sin⁡(x)+1)(1−1tan⁡(x)+1sin⁡(x))sin⁡(x)1+1tan⁡(x)−1sin⁡(x)\frac{\left(\sin{\left(x \right)} + 1\right) \left(1 - \frac{1}{\tan{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right) \sin{\left(x \right)}}{1 + \frac{1}{\tan{\left(x \right)}} - \frac{1}{\sin{\left(x \right)}}} 
             /      1            \       
(1 + sin(x))*|1 - ------ + csc(x)|*sin(x)
             \    tan(x)         /       
-----------------------------------------
                 1                       
           1 + ------ - csc(x)           
               tan(x)
(sin⁡(x)+1)(csc⁡(x)+1−1tan⁡(x))sin⁡(x)−csc⁡(x)+1+1tan⁡(x)\frac{\left(\sin{\left(x \right)} + 1\right) \left(\csc{\left(x \right)} + 1 - \frac{1}{\tan{\left(x \right)}}\right) \sin{\left(x \right)}}{- \csc{\left(x \right)} + 1 + \frac{1}{\tan{\left(x \right)}}} 
                2                                         
  /        2/x\\     4/x\              /       /x\\    /x\
2*|-1 + cot |-|| *sin |-|*(1 + sin(x))*|1 + tan|-||*tan|-|
  \         \4//      \4/              \       \2//    \2/
----------------------------------------------------------
                               /x\                        
                        1 - tan|-|                        
                               \2/
2(sin⁡(x)+1)(tan⁡(x2)+1)(cot⁡2(x4)−1)2sin⁡4(x4)tan⁡(x2)1−tan⁡(x2)\frac{2 \left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
/       /x\\                    
|    sin|-||                    
|       \2/|                    
|1 + ------|*(1 + sin(x))*sin(x)
|       /x\|                    
|    cos|-||                    
\       \2//                    
--------------------------------
                  /x\           
               sin|-|           
                  \2/           
           1 - ------           
                  /x\           
               cos|-|           
                  \2/
(sin⁡(x2)cos⁡(x2)+1)(sin⁡(x)+1)sin⁡(x)−sin⁡(x2)cos⁡(x2)+1\frac{\left(\frac{\sin{\left(\frac{x}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}} + 1\right) \left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{- \frac{\sin{\left(\frac{x}{2} \right)}}{\cos{\left(\frac{x}{2} \right)}} + 1} 
     4/x\    2/x\              /       /x\\
8*cos |-|*tan |-|*(1 + sin(x))*|1 + tan|-||
      \4/     \4/              \       \2//
-------------------------------------------
            /       /x\\    /x\            
            |1 - tan|-||*tan|-|            
            \       \2//    \2/
8(sin⁡(x)+1)(tan⁡(x2)+1)cos⁡4(x4)tan⁡2(x4)(1−tan⁡(x2))tan⁡(x2)\frac{8 \left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \cos^{4}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{4} \right)}}{\left(1 - \tan{\left(\frac{x}{2} \right)}\right) \tan{\left(\frac{x}{2} \right)}} 
               2                                         
  /       2/x\\     4/x\              /       /x\\    /x\
2*|1 - tan |-|| *cos |-|*(1 + sin(x))*|1 + tan|-||*tan|-|
  \        \4//      \4/              \       \2//    \2/
---------------------------------------------------------
                               /x\                       
                        1 - tan|-|                       
                               \2/
2(1−tan⁡2(x4))2(sin⁡(x)+1)(tan⁡(x2)+1)cos⁡4(x4)tan⁡(x2)1−tan⁡(x2)\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \cos^{4}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
     2/x\              /      1            \    /x\
2*sin |-|*(1 + sin(x))*|1 + ------ - cot(x)|*cot|-|
      \2/              \    sin(x)         /    \2/
---------------------------------------------------
                      1                            
                1 - ------ + cot(x)                
                    sin(x)
2(sin⁡(x)+1)(−cot⁡(x)+1+1sin⁡(x))sin⁡2(x2)cot⁡(x2)cot⁡(x)+1−1sin⁡(x)\frac{2 \left(\sin{\left(x \right)} + 1\right) \left(- \cot{\left(x \right)} + 1 + \frac{1}{\sin{\left(x \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)} \cot{\left(\frac{x}{2} \right)}}{\cot{\left(x \right)} + 1 - \frac{1}{\sin{\left(x \right)}}} 
          /           /x\ \             
          |      2*tan|-| |             
     2/x\ |           \2/ | /       /x\\
8*tan |-|*|1 + -----------|*|1 + tan|-||
      \4/ |           2/x\| \       \2//
          |    1 + tan |-||             
          \            \2//             
----------------------------------------
                2                       
   /       2/x\\  /       /x\\    /x\   
   |1 + tan |-|| *|1 - tan|-||*tan|-|   
   \        \4//  \       \2//    \2/
8(1+2tan⁡(x2)tan⁡2(x2)+1)(tan⁡(x2)+1)tan⁡2(x4)(1−tan⁡(x2))(tan⁡2(x4)+1)2tan⁡(x2)\frac{8 \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \tan^{2}{\left(\frac{x}{4} \right)}}{\left(1 - \tan{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan{\left(\frac{x}{2} \right)}} 
             /       /x\\
             |    sec|-||
/      1   \ |       \2/|
|1 + ------|*|1 + ------|
\    csc(x)/ |       /x\|
             |    csc|-||
             \       \2//
-------------------------
   /       /x\\          
   |    sec|-||          
   |       \2/|          
   |1 - ------|*csc(x)   
   |       /x\|          
   |    csc|-||          
   \       \2//
(1+sec⁡(x2)csc⁡(x2))(1+1csc⁡(x))(1−sec⁡(x2)csc⁡(x2))csc⁡(x)\frac{\left(1 + \frac{\sec{\left(\frac{x}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right) \left(1 + \frac{1}{\csc{\left(x \right)}}\right)}{\left(1 - \frac{\sec{\left(\frac{x}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right) \csc{\left(x \right)}} 
                  /       /    pi\              \
                  |    sec|x - --|              |
/         1     \ |       \    2 /      /    pi\|
|1 + -----------|*|1 - ----------- + sec|x - --||
|       /    pi\| \       sec(x)        \    2 //
|    sec|x - --||                                
\       \    2 //                                
-------------------------------------------------
   /                     /    pi\\               
   |                  sec|x - --||               
   |       /    pi\      \    2 /|    /    pi\   
   |1 - sec|x - --| + -----------|*sec|x - --|   
   \       \    2 /      sec(x)  /    \    2 /
(1+1sec⁡(x−π2))(sec⁡(x−π2)+1−sec⁡(x−π2)sec⁡(x))(−sec⁡(x−π2)+1+sec⁡(x−π2)sec⁡(x))sec⁡(x−π2)\frac{\left(1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \left(\sec{\left(x - \frac{\pi}{2} \right)} + 1 - \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right)}{\left(- \sec{\left(x - \frac{\pi}{2} \right)} + 1 + \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}} 
               /           /x\ \       
               |      2*cot|-| |       
  /      1   \ |           \2/ |    /x\
2*|1 + ------|*|1 + -----------|*cot|-|
  |       /x\| |           2/x\|    \2/
  |    cot|-|| |    1 + cot |-||       
  \       \2// \            \2//       
---------------------------------------
       /       2/x\\ /      1   \      
       |1 + cot |-||*|1 - ------|      
       \        \2// |       /x\|      
                     |    cot|-||      
                     \       \2//
2(1+2cot⁡(x2)cot⁡2(x2)+1)(1+1cot⁡(x2))cot⁡(x2)(1−1cot⁡(x2))(cot⁡2(x2)+1)\frac{2 \left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(1 + \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right) \cot{\left(\frac{x}{2} \right)}}{\left(1 - \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
               /       /x\\    /x\    /x\
2*(1 + sin(x))*|1 + tan|-||*cos|-|*sin|-|
               \       \2//    \2/    \2/
-----------------------------------------
                       /x\               
                1 - tan|-|               
                       \2/
2(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x2)cos⁡(x2)1−tan⁡(x2)\frac{2 \left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
                    /          /x\  \
                    |       sec|-|  |
  /         1     \ |          \2/  |
2*|1 + -----------|*|1 + -----------|
  |       /    pi\| |       /x   pi\|
  |    sec|x - --|| |    sec|- - --||
  \       \    2 // \       \2   2 //
-------------------------------------
 /          /x\  \                   
 |       sec|-|  |                   
 |          \2/  |    /x\    /x   pi\
 |1 - -----------|*sec|-|*sec|- - --|
 |       /x   pi\|    \2/    \2   2 /
 |    sec|- - --||                   
 \       \2   2 //
2(1+1sec⁡(x−π2))(sec⁡(x2)sec⁡(x2−π2)+1)(−sec⁡(x2)sec⁡(x2−π2)+1)sec⁡(x2)sec⁡(x2−π2)\frac{2 \left(1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \left(\frac{\sec{\left(\frac{x}{2} \right)}}{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)}{\left(- \frac{\sec{\left(\frac{x}{2} \right)}}{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{x}{2} \right)} \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} 
     2/x\    4/x\              /       /x\\    /x\
8*cot |-|*sin |-|*(1 + sin(x))*|1 + tan|-||*cot|-|
      \4/     \4/              \       \2//    \2/
--------------------------------------------------
                           /x\                    
                    1 - tan|-|                    
                           \2/
8(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡4(x4)cot⁡2(x4)cot⁡(x2)1−tan⁡(x2)\frac{8 \left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin^{4}{\left(\frac{x}{4} \right)} \cot^{2}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
/      1   \ /       csc(x)           \
|1 + ------|*|1 - ----------- + csc(x)|
\    csc(x)/ |       /pi    \         |
             |    csc|-- - x|         |
             \       \2     /         /
---------------------------------------
   /                csc(x)  \          
   |1 - csc(x) + -----------|*csc(x)   
   |                /pi    \|          
   |             csc|-- - x||          
   \                \2     //
(1+1csc⁡(x))(csc⁡(x)−csc⁡(x)csc⁡(−x+π2)+1)(−csc⁡(x)+csc⁡(x)csc⁡(−x+π2)+1)csc⁡(x)\frac{\left(1 + \frac{1}{\csc{\left(x \right)}}\right) \left(\csc{\left(x \right)} - \frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + 1\right)}{\left(- \csc{\left(x \right)} + \frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(x \right)}} 
                 /       /pi   x\\  
                 |    csc|-- - -||  
    /      1   \ |       \2    2/|  
  2*|1 + ------|*|1 + -----------|  
    \    csc(x)/ |          /x\  |  
                 |       csc|-|  |  
                 \          \2/  /  
------------------------------------
/       /pi   x\\                   
|    csc|-- - -||                   
|       \2    2/|    /x\    /pi   x\
|1 - -----------|*csc|-|*csc|-- - -|
|          /x\  |    \2/    \2    2/
|       csc|-|  |                   
\          \2/  /
2(1+csc⁡(−x2+π2)csc⁡(x2))(1+1csc⁡(x))(1−csc⁡(−x2+π2)csc⁡(x2))csc⁡(x2)csc⁡(−x2+π2)\frac{2 \left(1 + \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right) \left(1 + \frac{1}{\csc{\left(x \right)}}\right)}{\left(1 - \frac{\csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{x}{2} \right)}}\right) \csc{\left(\frac{x}{2} \right)} \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} 
                       /           /x\ \       
                       |      2*cot|-| |       
     2/x\ /      1   \ |           \2/ |    /x\
8*cot |-|*|1 + ------|*|1 + -----------|*cot|-|
      \4/ |       /x\| |           2/x\|    \2/
          |    cot|-|| |    1 + cot |-||       
          \       \2// \            \2//       
-----------------------------------------------
                       2                       
          /       2/x\\  /      1   \          
          |1 + cot |-|| *|1 - ------|          
          \        \4//  |       /x\|          
                         |    cot|-||          
                         \       \2//
8(1+2cot⁡(x2)cot⁡2(x2)+1)(1+1cot⁡(x2))cot⁡2(x4)cot⁡(x2)(1−1cot⁡(x2))(cot⁡2(x4)+1)2\frac{8 \left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(1 + \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right) \cot^{2}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{\left(1 - \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} 
  /           /x\ \ /                    2/x\\       
  |      2*cot|-| | |             1 + cot |-||       
  |           \2/ | |                     \2/|    /x\
2*|1 + -----------|*|1 - cot(x) + -----------|*cot|-|
  |           2/x\| |                    /x\ |    \2/
  |    1 + cot |-|| |               2*cot|-| |       
  \            \2// \                    \2/ /       
-----------------------------------------------------
                     /           2/x\         \      
                     |    1 + cot |-|         |      
       /       2/x\\ |            \2/         |      
       |1 + cot |-||*|1 - ----------- + cot(x)|      
       \        \2// |           /x\          |      
                     |      2*cot|-|          |      
                     \           \2/          /
2(1+2cot⁡(x2)cot⁡2(x2)+1)(cot⁡2(x2)+12cot⁡(x2)−cot⁡(x)+1)cot⁡(x2)(cot⁡2(x2)+1)(−cot⁡2(x2)+12cot⁡(x2)+cot⁡(x)+1)\frac{2 \left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{2 \cot{\left(\frac{x}{2} \right)}} - \cot{\left(x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(- \frac{\cot^{2}{\left(\frac{x}{2} \right)} + 1}{2 \cot{\left(\frac{x}{2} \right)}} + \cot{\left(x \right)} + 1\right)} 
/       /    pi\\ /         1           cos(x)  \    /    pi\
|1 + cos|x - --||*|1 + ----------- - -----------|*cos|x - --|
\       \    2 // |       /    pi\      /    pi\|    \    2 /
                  |    cos|x - --|   cos|x - --||            
                  \       \    2 /      \    2 //            
-------------------------------------------------------------
                         1           cos(x)                  
                1 - ----------- + -----------                
                       /    pi\      /    pi\                
                    cos|x - --|   cos|x - --|                
                       \    2 /      \    2 /
(cos⁡(x−π2)+1)(−cos⁡(x)cos⁡(x−π2)+1+1cos⁡(x−π2))cos⁡(x−π2)cos⁡(x)cos⁡(x−π2)+1−1cos⁡(x−π2)\frac{\left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right) \left(- \frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + 1 + \frac{1}{\cos{\left(x - \frac{\pi}{2} \right)}}\right) \cos{\left(x - \frac{\pi}{2} \right)}}{\frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + 1 - \frac{1}{\cos{\left(x - \frac{\pi}{2} \right)}}} 
     2/x\              /       /x\\    /x\
2*sin |-|*(1 + sin(x))*|1 + tan|-||*cot|-|
      \2/              \       \2//    \2/
------------------------------------------
                       /x\                
                1 - tan|-|                
                       \2/
2(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡2(x2)cot⁡(x2)1−tan⁡(x2)\frac{2 \left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin^{2}{\left(\frac{x}{2} \right)} \cot{\left(\frac{x}{2} \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
             /      1       sin(2*x)\       
(1 + sin(x))*|1 + ------ - ---------|*sin(x)
             |    sin(x)        2   |       
             \             2*sin (x)/       
--------------------------------------------
                 1       sin(2*x)           
           1 - ------ + ---------           
               sin(x)        2              
                        2*sin (x)
(sin⁡(x)+1)(1+1sin⁡(x)−sin⁡(2x)2sin⁡2(x))sin⁡(x)1−1sin⁡(x)+sin⁡(2x)2sin⁡2(x)\frac{\left(\sin{\left(x \right)} + 1\right) \left(1 + \frac{1}{\sin{\left(x \right)}} - \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}\right) \sin{\left(x \right)}}{1 - \frac{1}{\sin{\left(x \right)}} + \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}} 
                  /          /x\  \
                  |       sec|-|  |
/         1     \ |          \2/  |
|1 + -----------|*|1 + -----------|
|       /    pi\| |       /x   pi\|
|    sec|x - --|| |    sec|- - --||
\       \    2 // \       \2   2 //
-----------------------------------
   /          /x\  \               
   |       sec|-|  |               
   |          \2/  |    /    pi\   
   |1 - -----------|*sec|x - --|   
   |       /x   pi\|    \    2 /   
   |    sec|- - --||               
   \       \2   2 //
(1+1sec⁡(x−π2))(sec⁡(x2)sec⁡(x2−π2)+1)(−sec⁡(x2)sec⁡(x2−π2)+1)sec⁡(x−π2)\frac{\left(1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \left(\frac{\sec{\left(\frac{x}{2} \right)}}{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)}{\left(- \frac{\sec{\left(\frac{x}{2} \right)}}{\sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}} 
                  /                                   ___    /    pi\\
                  |                                 \/ 2 *cos|x + --||
     2/x\    2/x\ |      1        ___    /    pi\            \    4 /|
4*cos |-|*sin |-|*|1 + ------ - \/ 2 *cos|x + --| - -----------------|
      \2/     \2/ \    sin(x)            \    4 /         sin(x)     /
----------------------------------------------------------------------
                               ___    /    pi\                        
                        -1 + \/ 2 *sin|x + --|                        
                                      \    4 /
4(−2cos⁡(x+π4)+1−2cos⁡(x+π4)sin⁡(x)+1sin⁡(x))sin⁡2(x2)cos⁡2(x2)2sin⁡(x+π4)−1\frac{4 \left(- \sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)} + 1 - \frac{\sqrt{2} \cos{\left(x + \frac{\pi}{4} \right)}}{\sin{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)} \cos^{2}{\left(\frac{x}{2} \right)}}{\sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)} - 1} 
                               /           /x\ \
                2              |      2*cot|-| |
  /        2/x\\  /      1   \ |           \2/ |
2*|-1 + cot |-|| *|1 + ------|*|1 + -----------|
  \         \4//  |       /x\| |           2/x\|
                  |    cot|-|| |    1 + cot |-||
                  \       \2// \            \2//
------------------------------------------------
                    2                           
       /       2/x\\  /      1   \    /x\       
       |1 + cot |-|| *|1 - ------|*cot|-|       
       \        \4//  |       /x\|    \2/       
                      |    cot|-||              
                      \       \2//
2(1+2cot⁡(x2)cot⁡2(x2)+1)(1+1cot⁡(x2))(cot⁡2(x4)−1)2(1−1cot⁡(x2))(cot⁡2(x4)+1)2cot⁡(x2)\frac{2 \left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(1 + \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2}}{\left(1 - \frac{1}{\cot{\left(\frac{x}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}} 
/         2/x\\                    
|    2*sin |-||                    
|          \2/|                    
|1 + ---------|*(1 + sin(x))*sin(x)
\      sin(x) /                    
-----------------------------------
                    2/x\           
               2*sin |-|           
                     \2/           
           1 - ---------           
                 sin(x)
(2sin⁡2(x2)sin⁡(x)+1)(sin⁡(x)+1)sin⁡(x)−2sin⁡2(x2)sin⁡(x)+1\frac{\left(\frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + 1\right) \left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{- \frac{2 \sin^{2}{\left(\frac{x}{2} \right)}}{\sin{\left(x \right)}} + 1} 
  /           /x\ \                    
  |      2*tan|-| |                    
  |           \2/ | /       /x\\    /x\
2*|1 + -----------|*|1 + tan|-||*tan|-|
  |           2/x\| \       \2//    \2/
  |    1 + tan |-||                    
  \            \2//                    
---------------------------------------
       /       2/x\\ /       /x\\      
       |1 + tan |-||*|1 - tan|-||      
       \        \2// \       \2//
2(1+2tan⁡(x2)tan⁡2(x2)+1)(tan⁡(x2)+1)tan⁡(x2)(1−tan⁡(x2))(tan⁡2(x2)+1)\frac{2 \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}{\left(1 - \tan{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} 
2*(1 + 2*tan(x/2)/(1 + tan(x/2)^2))*(1 + tan(x/2))*tan(x/2)/((1 + tan(x/2)^2)*(1 - tan(x/2)))
Abrimos la expresión [src] 
             /       /x\\       
(1 + sin(x))*|1 + tan|-||*sin(x)
             \       \2//       
--------------------------------
                  /x\           
           1 - tan|-|           
                  \2/
(sin⁡(x)+1)(tan⁡(x2)+1)sin⁡(x)1−tan⁡(x2)\frac{\left(\sin{\left(x \right)} + 1\right) \left(\tan{\left(\frac{x}{2} \right)} + 1\right) \sin{\left(x \right)}}{1 - \tan{\left(\frac{x}{2} \right)}} 
           2                                     
        sin (x)                    sin(x)        
----------------------- + -----------------------
                  /x\                       /x\  
               tan|-|                    tan|-|  
    1             \2/         1             \2/  
---------- - ----------   ---------- - ----------
       /x\          /x\          /x\          /x\
1 + tan|-|   1 + tan|-|   1 + tan|-|   1 + tan|-|
       \2/          \2/          \2/          \2/
sin⁡2(x)−tan⁡(x2)tan⁡(x2)+1+1tan⁡(x2)+1+sin⁡(x)−tan⁡(x2)tan⁡(x2)+1+1tan⁡(x2)+1\frac{\sin^{2}{\left(x \right)}}{- \frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(\frac{x}{2} \right)} + 1} + \frac{1}{\tan{\left(\frac{x}{2} \right)} + 1}} + \frac{\sin{\left(x \right)}}{- \frac{\tan{\left(\frac{x}{2} \right)}}{\tan{\left(\frac{x}{2} \right)} + 1} + \frac{1}{\tan{\left(\frac{x}{2} \right)} + 1}} 
sin(x)^2/(1/(1 + tan(x/2)) - tan(x/2)/(1 + tan(x/2))) + sin(x)/(1/(1 + tan(x/2)) - tan(x/2)/(1 + tan(x/2)))
    © Sr Examen – Калькулятор