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

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

Expresión a simplificar:

Solución

Ha introducido [src] 
   2               
cos (x)*a          
---------- - sin(a)
1 - sin(a)
acos⁡2(x)1−sin⁡(a)−sin⁡(a)\frac{a \cos^{2}{\left(x \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
(cos(x)^2*a)/(1 - sin(a)) - sin(a)
Simplificación general [src] 
        2           2            
-1 + cos (a) - a*cos (x) + sin(a)
---------------------------------
           -1 + sin(a)
−acos⁡2(x)+sin⁡(a)+cos⁡2(a)−1sin⁡(a)−1\frac{- a \cos^{2}{\left(x \right)} + \sin{\left(a \right)} + \cos^{2}{\left(a \right)} - 1}{\sin{\left(a \right)} - 1} 
(-1 + cos(a)^2 - a*cos(x)^2 + sin(a))/(-1 + sin(a))
Respuesta numérica [src] 
-sin(a) + a*cos(x)^2/(1.0 - sin(a))
-sin(a) + a*cos(x)^2/(1.0 - sin(a))
Combinatoria [src] 
 /   2                    2   \ 
-\sin (a) - sin(a) + a*cos (x)/ 
--------------------------------
          -1 + sin(a)
−acos⁡2(x)+sin⁡2(a)−sin⁡(a)sin⁡(a)−1- \frac{a \cos^{2}{\left(x \right)} + \sin^{2}{\left(a \right)} - \sin{\left(a \right)}}{\sin{\left(a \right)} - 1} 
-(sin(a)^2 - sin(a) + a*cos(x)^2)/(-1 + sin(a))
Denominador común [src] 
                2    
           a*cos (x) 
-sin(a) - -----------
          -1 + sin(a)
−acos⁡2(x)sin⁡(a)−1−sin⁡(a)- \frac{a \cos^{2}{\left(x \right)}}{\sin{\left(a \right)} - 1} - \sin{\left(a \right)} 
-sin(a) - a*cos(x)^2/(-1 + sin(a))
Denominador racional [src] 
     2                         
a*cos (x) - (1 - sin(a))*sin(a)
-------------------------------
           1 - sin(a)
acos⁡2(x)−(1−sin⁡(a))sin⁡(a)1−sin⁡(a)\frac{a \cos^{2}{\left(x \right)} - \left(1 - \sin{\left(a \right)}\right) \sin{\left(a \right)}}{1 - \sin{\left(a \right)}} 
(a*cos(x)^2 - (1 - sin(a))*sin(a))/(1 - sin(a))
Unión de expresiones racionales [src] 
     2                         
a*cos (x) - (1 - sin(a))*sin(a)
-------------------------------
           1 - sin(a)
acos⁡2(x)−(1−sin⁡(a))sin⁡(a)1−sin⁡(a)\frac{a \cos^{2}{\left(x \right)} - \left(1 - \sin{\left(a \right)}\right) \sin{\left(a \right)}}{1 - \sin{\left(a \right)}} 
(a*cos(x)^2 - (1 - sin(a))*sin(a))/(1 - sin(a))
Parte trigonométrica [src] 
                     2       4/x\    
              4*a*cos (x)*sin |-|    
                              \2/    
-sin(a) + ---------------------------
                                    2
          (1 - sin(a))*(-1 + cos(x))
4asin⁡4(x2)cos⁡2(x)(1−sin⁡(a))(cos⁡(x)−1)2−sin⁡(a)\frac{4 a \sin^{4}{\left(\frac{x}{2} \right)} \cos^{2}{\left(x \right)}}{\left(1 - \sin{\left(a \right)}\right) \left(\cos{\left(x \right)} - 1\right)^{2}} - \sin{\left(a \right)} 
                                       2        
         /a\              /       2/x\\         
    2*tan|-|            a*|1 - tan |-||         
         \2/              \        \2//         
- ----------- + --------------------------------
         2/a\                  /           /a\ \
  1 + tan |-|                2 |      2*tan|-| |
          \2/   /       2/x\\  |           \2/ |
                |1 + tan |-|| *|1 - -----------|
                \        \2//  |           2/a\|
                               |    1 + tan |-||
                               \            \2//
a(1−tan⁡2(x2))2(1−2tan⁡(a2)tan⁡2(a2)+1)(tan⁡2(x2)+1)2−2tan⁡(a2)tan⁡2(a2)+1\frac{a \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\left(1 - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} 
                                     2          
         /a\           /        2/x\\     4/x\  
    2*cot|-|      16*a*|-1 + cot |-|| *cot |-|  
         \2/           \         \2//      \4/  
- ----------- + --------------------------------
         2/a\                  /           /a\ \
  1 + cot |-|                4 |      2*cot|-| |
          \2/   /       2/x\\  |           \2/ |
                |1 + cot |-|| *|1 - -----------|
                \        \4//  |           2/a\|
                               |    1 + cot |-||
                               \            \2//
16a(cot⁡2(x2)−1)2cot⁡4(x4)(1−2cot⁡(a2)cot⁡2(a2)+1)(cot⁡2(x4)+1)4−2cot⁡(a2)cot⁡2(a2)+1\frac{16 a \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \cot^{4}{\left(\frac{x}{4} \right)}}{\left(1 - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} 
                           2             
            /         4/x\\              
            |    4*sin |-||              
            |          \2/|     4/pi   x\
          a*|1 - ---------| *sin |-- + -|
            |        2    |      \2    2/
            \     sin (x) /              
-sin(a) + -------------------------------
                     1 - sin(a)
a(−4sin⁡4(x2)sin⁡2(x)+1)2sin⁡4(x2+π2)1−sin⁡(a)−sin⁡(a)\frac{a \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right)^{2} \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
                                      2  
                    /         2/x\   \   
                    |      sec |-|   |   
                    |          \2/   |   
                  a*|1 - ------------|   
                    |       2/x   pi\|   
                    |    sec |- - --||   
       1            \        \2   2 //   
- ----------- + -------------------------
     /    pi\   /         1     \    4/x\
  sec|a - --|   |1 - -----------|*sec |-|
     \    2 /   |       /    pi\|     \2/
                |    sec|a - --||        
                \       \    2 //
a(−sec⁡2(x2)sec⁡2(x2−π2)+1)2(1−1sec⁡(a−π2))sec⁡4(x2)−1sec⁡(a−π2)\frac{a \left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\left(1 - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec^{4}{\left(\frac{x}{2} \right)}} - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} 
                             2                
               /        1   \     8/x\    4/x\
          16*a*|-1 + -------| *cos |-|*tan |-|
               |        2/x\|      \4/     \4/
               |     tan |-||                 
               \         \2//                 
-sin(a) + ------------------------------------
                       1 - sin(a)
16a(−1+1tan⁡2(x2))2cos⁡8(x4)tan⁡4(x4)1−sin⁡(a)−sin⁡(a)\frac{16 a \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \cos^{8}{\left(\frac{x}{4} \right)} \tan^{4}{\left(\frac{x}{4} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
          a*(1 + cos(2*x))
-sin(a) - ----------------
          2*(-1 + sin(a))
−a(cos⁡(2x)+1)2(sin⁡(a)−1)−sin⁡(a)- \frac{a \left(\cos{\left(2 x \right)} + 1\right)}{2 \left(\sin{\left(a \right)} - 1\right)} - \sin{\left(a \right)} 
                         2              4        
            /       2/x\\  /       2/x\\     8/x\
          a*|1 - tan |-|| *|1 - tan |-|| *cos |-|
            \        \2//  \        \4//      \4/
-sin(a) + ---------------------------------------
                         1 - sin(a)
a(1−tan⁡2(x4))4(1−tan⁡2(x2))2cos⁡8(x4)1−sin⁡(a)−sin⁡(a)\frac{a \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \cos^{8}{\left(\frac{x}{4} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
    1                  a            
- ------ + -------------------------
  csc(a)   /      1   \    2/pi    \
           |1 - ------|*csc |-- - x|
           \    csc(a)/     \2     /
a(1−1csc⁡(a))csc⁡2(−x+π2)−1csc⁡(a)\frac{a}{\left(1 - \frac{1}{\csc{\left(a \right)}}\right) \csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(a \right)}} 
                         2               4        
            /       2/x\\  /        2/x\\     8/x\
          a*|1 - tan |-|| *|-1 + cot |-|| *sin |-|
            \        \2//  \         \4//      \4/
-sin(a) + ----------------------------------------
                         1 - sin(a)
a(1−tan⁡2(x2))2(cot⁡2(x4)−1)4sin⁡8(x4)1−sin⁡(a)−sin⁡(a)\frac{a \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{x}{4} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
                                       2        
         /a\             /        2/x\\         
    2*cot|-|           a*|-1 + cot |-||         
         \2/             \         \2//         
- ----------- + --------------------------------
         2/a\                  /           /a\ \
  1 + cot |-|                2 |      2*cot|-| |
          \2/   /       2/x\\  |           \2/ |
                |1 + cot |-|| *|1 - -----------|
                \        \2//  |           2/a\|
                               |    1 + cot |-||
                               \            \2//
a(cot⁡2(x2)−1)2(1−2cot⁡(a2)cot⁡2(a2)+1)(cot⁡2(x2)+1)2−2cot⁡(a2)cot⁡2(a2)+1\frac{a \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\left(1 - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} 
                        2      
     /    pi\      a*cos (x)   
- cos|a - --| + ---------------
     \    2 /          /    pi\
                1 - cos|a - --|
                       \    2 /
acos⁡2(x)1−cos⁡(a−π2)−cos⁡(a−π2)\frac{a \cos^{2}{\left(x \right)}}{1 - \cos{\left(a - \frac{\pi}{2} \right)}} - \cos{\left(a - \frac{\pi}{2} \right)} 
                                 2  
               /       2/pi   x\\   
               |    csc |-- - -||   
               |        \2    2/|   
             a*|1 - ------------|   
               |         2/x\   |   
               |      csc |-|   |   
    1          \          \2/   /   
- ------ + -------------------------
  csc(a)   /      1   \    4/pi   x\
           |1 - ------|*csc |-- - -|
           \    csc(a)/     \2    2/
a(1−csc⁡2(−x2+π2)csc⁡2(x2))2(1−1csc⁡(a))csc⁡4(−x2+π2)−1csc⁡(a)\frac{a \left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)^{2}}{\left(1 - \frac{1}{\csc{\left(a \right)}}\right) \csc^{4}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(a \right)}} 
                                2
             /          2/x\   \ 
             |       csc |-|   | 
             |           \2/   | 
           a*|-1 + ------------| 
             |        2/pi   x\| 
             |     csc |-- - -|| 
    1        \         \2    2// 
- ------ + ----------------------
  csc(a)    /      1   \    4/x\ 
            |1 - ------|*csc |-| 
            \    csc(a)/     \2/
a(csc⁡2(x2)csc⁡2(−x2+π2)−1)2(1−1csc⁡(a))csc⁡4(x2)−1csc⁡(a)\frac{a \left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(1 - \frac{1}{\csc{\left(a \right)}}\right) \csc^{4}{\left(\frac{x}{2} \right)}} - \frac{1}{\csc{\left(a \right)}} 
                                     2             
                  /          2/x\   \              
                  |       cos |-|   |              
                  |           \2/   |     4/x   pi\
                a*|-1 + ------------| *cos |- - --|
                  |        2/x   pi\|      \2   2 /
                  |     cos |- - --||              
     /    pi\     \         \2   2 //              
- cos|a - --| + -----------------------------------
     \    2 /                    /    pi\          
                          1 - cos|a - --|          
                                 \    2 /
a(cos⁡2(x2)cos⁡2(x2−π2)−1)2cos⁡4(x2−π2)1−cos⁡(a−π2)−cos⁡(a−π2)\frac{a \left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2} \cos^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{1 - \cos{\left(a - \frac{\pi}{2} \right)}} - \cos{\left(a - \frac{\pi}{2} \right)} 
                                     2          
                       /        1   \     4/x\  
                  16*a*|-1 + -------| *tan |-|  
         /a\           |        2/x\|      \4/  
    2*tan|-|           |     tan |-||           
         \2/           \         \2//           
- ----------- + --------------------------------
         2/a\                  /           /a\ \
  1 + tan |-|                4 |      2*tan|-| |
          \2/   /       2/x\\  |           \2/ |
                |1 + tan |-|| *|1 - -----------|
                \        \4//  |           2/a\|
                               |    1 + tan |-||
                               \            \2//
16a(−1+1tan⁡2(x2))2tan⁡4(x4)(1−2tan⁡(a2)tan⁡2(a2)+1)(tan⁡2(x4)+1)4−2tan⁡(a2)tan⁡2(a2)+1\frac{16 a \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \tan^{4}{\left(\frac{x}{4} \right)}}{\left(1 - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} 
                             2                
               /        2/x\\     4/x\    8/x\
          16*a*|-1 + cot |-|| *cot |-|*sin |-|
               \         \2//      \4/     \4/
-sin(a) + ------------------------------------
                       1 - sin(a)
16a(cot⁡2(x2)−1)2sin⁡8(x4)cot⁡4(x4)1−sin⁡(a)−sin⁡(a)\frac{16 a \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \sin^{8}{\left(\frac{x}{4} \right)} \cot^{4}{\left(\frac{x}{4} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
                                    2        
                  /       2/x   pi\\         
                  |    cos |- - --||         
                  |        \2   2 /|     4/x\
                a*|1 - ------------| *cos |-|
                  |         2/x\   |      \2/
                  |      cos |-|   |         
     /    pi\     \          \2/   /         
- cos|a - --| + -----------------------------
     \    2 /                 /    pi\       
                       1 - cos|a - --|       
                              \    2 /
a(1−cos⁡2(x2−π2)cos⁡2(x2))2cos⁡4(x2)1−cos⁡(a−π2)−cos⁡(a−π2)\frac{a \left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \cos^{4}{\left(\frac{x}{2} \right)}}{1 - \cos{\left(a - \frac{\pi}{2} \right)}} - \cos{\left(a - \frac{\pi}{2} \right)} 
                               2               4
                  /       1   \  /        2/x\\ 
                a*|1 - -------| *|-1 + cot |-|| 
         /a\      |       2/x\|  \         \4// 
    2*cot|-|      |    cot |-||                 
         \2/      \        \2//                 
- ----------- + --------------------------------
         2/a\                  /           /a\ \
  1 + cot |-|                4 |      2*cot|-| |
          \2/   /       2/x\\  |           \2/ |
                |1 + cot |-|| *|1 - -----------|
                \        \4//  |           2/a\|
                               |    1 + cot |-||
                               \            \2//
a(1−1cot⁡2(x2))2(cot⁡2(x4)−1)4(1−2cot⁡(a2)cot⁡2(a2)+1)(cot⁡2(x4)+1)4−2cot⁡(a2)cot⁡2(a2)+1\frac{a \left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{4}}{\left(1 - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} 
                          2        
            /        2/x\\     4/x\
          a*|-1 + cot |-|| *sin |-|
            \         \2//      \2/
-sin(a) + -------------------------
                  1 - sin(a)
a(cot⁡2(x2)−1)2sin⁡4(x2)1−sin⁡(a)−sin⁡(a)\frac{a \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{2} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
                            2        
            /         2    \         
            |      sin (x) |     4/x\
          a*|-1 + ---------| *sin |-|
            |          4/x\|      \2/
            |     4*sin |-||         
            \           \2//         
-sin(a) + ---------------------------
                   1 - sin(a)
a(−1+sin⁡2(x)4sin⁡4(x2))2sin⁡4(x2)1−sin⁡(a)−sin⁡(a)\frac{a \left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{x}{2} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
                               2              4 
         /a\      /       2/x\\  /       2/x\\  
    2*tan|-|    a*|1 - tan |-|| *|1 - tan |-||  
         \2/      \        \2//  \        \4//  
- ----------- + --------------------------------
         2/a\                  /           /a\ \
  1 + tan |-|                4 |      2*tan|-| |
          \2/   /       2/x\\  |           \2/ |
                |1 + tan |-|| *|1 - -----------|
                \        \4//  |           2/a\|
                               |    1 + tan |-||
                               \            \2//
a(1−tan⁡2(x4))4(1−tan⁡2(x2))2(1−2tan⁡(a2)tan⁡2(a2)+1)(tan⁡2(x4)+1)4−2tan⁡(a2)tan⁡2(a2)+1\frac{a \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\left(1 - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} 
                                         2    
                      /        2/x   pi\\     
                      |     sec |- - --||     
                      |         \2   2 /|     
                    a*|-1 + ------------|     
                      |          2/x\   |     
                      |       sec |-|   |     
       1              \           \2/   /     
- ----------- + ------------------------------
     /    pi\   /         1     \    4/x   pi\
  sec|a - --|   |1 - -----------|*sec |- - --|
     \    2 /   |       /    pi\|     \2   2 /
                |    sec|a - --||             
                \       \    2 //
a(−1+sec⁡2(x2−π2)sec⁡2(x2))2(1−1sec⁡(a−π2))sec⁡4(x2−π2)−1sec⁡(a−π2)\frac{a \left(-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right)^{2}}{\left(1 - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec^{4}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} 
                         2        
            /       2/x\\     4/x\
          a*|1 - tan |-|| *cos |-|
            \        \2//      \2/
-sin(a) + ------------------------
                 1 - sin(a)
a(1−tan⁡2(x2))2cos⁡4(x2)1−sin⁡(a)−sin⁡(a)\frac{a \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \cos^{4}{\left(\frac{x}{2} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
                          2        
            /        1   \     4/x\
          a*|-1 + -------| *sin |-|
            |        2/x\|      \2/
            |     tan |-||         
            \         \2//         
-sin(a) + -------------------------
                  1 - sin(a)
a(−1+1tan⁡2(x2))2sin⁡4(x2)1−sin⁡(a)−sin⁡(a)\frac{a \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{x}{2} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
    1               a          
- ------ + --------------------
  csc(a)   /      1   \    2   
           |1 - ------|*sec (x)
           \    csc(a)/
a(1−1csc⁡(a))sec⁡2(x)−1csc⁡(a)\frac{a}{\left(1 - \frac{1}{\csc{\left(a \right)}}\right) \sec^{2}{\left(x \right)}} - \frac{1}{\csc{\left(a \right)}} 
       1                    a            
- ----------- + -------------------------
     /    pi\   /         1     \    2   
  sec|a - --|   |1 - -----------|*sec (x)
     \    2 /   |       /    pi\|        
                |    sec|a - --||        
                \       \    2 //
a(1−1sec⁡(a−π2))sec⁡2(x)−1sec⁡(a−π2)\frac{a}{\left(1 - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec^{2}{\left(x \right)}} - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} 
                    2       4/x\    
             4*a*cos (x)*cos |-|    
                             \2/    
-sin(a) + --------------------------
                                   2
          (1 - sin(a))*(1 + cos(x))
4acos⁡4(x2)cos⁡2(x)(1−sin⁡(a))(cos⁡(x)+1)2−sin⁡(a)\frac{4 a \cos^{4}{\left(\frac{x}{2} \right)} \cos^{2}{\left(x \right)}}{\left(1 - \sin{\left(a \right)}\right) \left(\cos{\left(x \right)} + 1\right)^{2}} - \sin{\left(a \right)} 
               2/    pi\
          a*sin |x + --|
                \    2 /
-sin(a) + --------------
            1 - sin(a)
asin⁡2(x+π2)1−sin⁡(a)−sin⁡(a)\frac{a \sin^{2}{\left(x + \frac{\pi}{2} \right)}}{1 - \sin{\left(a \right)}} - \sin{\left(a \right)} 
-sin(a) + a*sin(x + pi/2)^2/(1 - sin(a))
Potencias [src] 
                                       2   
                         / I*x    -I*x\    
                         |e      e    |    
  /   -I*a    I*a\     a*|---- + -----|    
I*\- e     + e   /       \ 2       2  /    
------------------ + ----------------------
        2                  /   -I*a    I*a\
                         I*\- e     + e   /
                     1 + ------------------
                                 2
a(eix2+e−ix2)2i(eia−e−ia)2+1+i(eia−e−ia)2\frac{a \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{\frac{i \left(e^{i a} - e^{- i a}\right)}{2} + 1} + \frac{i \left(e^{i a} - e^{- i a}\right)}{2} 
i*(-exp(-i*a) + exp(i*a))/2 + a*(exp(i*x)/2 + exp(-i*x)/2)^2/(1 + i*(-exp(-i*a) + exp(i*a))/2)
    © Sr Examen – Калькулятор