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Simplificación de expresiones/ Descomposición en fracciones simples/ sin(a)*(-cos(a))*(-cos(2*a))/((cos(4)*a))

¿Cómo vas a descomponer esta sin(a)*(-cos(a))*(-cos(2*a))/((cos(4)*a)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
sin(a)*(-cos(a))*(-cos(2*a))
----------------------------
          cos(4)*a
sin⁡(a)(−cos⁡(a))(−cos⁡(2a))acos⁡(4)\frac{\sin{\left(a \right)} \left(- \cos{\left(a \right)}\right) \left(- \cos{\left(2 a \right)}\right)}{a \cos{\left(4 \right)}} 
((sin(a)*(-cos(a)))*(-cos(2*a)))/((cos(4)*a))
Simplificación general [src] 
 sin(4*a) 
----------
4*a*cos(4)
sin⁡(4a)4acos⁡(4)\frac{\sin{\left(4 a \right)}}{4 a \cos{\left(4 \right)}} 
sin(4*a)/(4*a*cos(4))
Respuesta numérica [src] 
-1.5298856564664*cos(a)*cos(2*a)*sin(a)/a
-1.5298856564664*cos(a)*cos(2*a)*sin(a)/a
Denominador común [src] 
cos(a)*cos(2*a)*sin(a)
----------------------
       a*cos(4)
sin⁡(a)cos⁡(a)cos⁡(2a)acos⁡(4)\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}} 
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Combinatoria [src] 
cos(a)*cos(2*a)*sin(a)
----------------------
       a*cos(4)
sin⁡(a)cos⁡(a)cos⁡(2a)acos⁡(4)\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}} 
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Denominador racional [src] 
cos(a)*cos(2*a)*sin(a)
----------------------
       a*cos(4)
sin⁡(a)cos⁡(a)cos⁡(2a)acos⁡(4)\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}} 
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Abrimos la expresión [src] 
                                              3                
          cos(a)*sin(a)                  2*cos (a)*sin(a)      
- ----------------------------- + -----------------------------
             2             4                 2             4   
  a - 8*a*cos (1) + 8*a*cos (1)   a - 8*a*cos (1) + 8*a*cos (1)
2sin⁡(a)cos⁡3(a)−8acos⁡2(1)+8acos⁡4(1)+a−sin⁡(a)cos⁡(a)−8acos⁡2(1)+8acos⁡4(1)+a\frac{2 \sin{\left(a \right)} \cos^{3}{\left(a \right)}}{- 8 a \cos^{2}{\left(1 \right)} + 8 a \cos^{4}{\left(1 \right)} + a} - \frac{\sin{\left(a \right)} \cos{\left(a \right)}}{- 8 a \cos^{2}{\left(1 \right)} + 8 a \cos^{4}{\left(1 \right)} + a} 
cos(a)*cos(2*a)*sin(a)
----------------------
       a*cos(4)
sin⁡(a)cos⁡(a)cos⁡(2a)acos⁡(4)\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}} 
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Unión de expresiones racionales [src] 
cos(a)*cos(2*a)*sin(a)
----------------------
       a*cos(4)
sin⁡(a)cos⁡(a)cos⁡(2a)acos⁡(4)\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}} 
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Compilar la expresión [src] 
cos(a)*cos(2*a)*sin(a)
----------------------
       a*cos(4)
sin⁡(a)cos⁡(a)cos⁡(2a)acos⁡(4)\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}} 
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Parte trigonométrica [src] 
     2       4/a\ /       2   \ /       2/a\\    /a\
2*cos (a)*cos |-|*\1 - tan (a)/*|1 - tan |-||*tan|-|
              \2/               \        \2//    \2/
----------------------------------------------------
                /       2   \    2                  
              a*\1 - tan (2)/*cos (2)
2(1−tan⁡2(a2))(1−tan⁡2(a))cos⁡4(a2)cos⁡2(a)tan⁡(a2)a(1−tan⁡2(2))cos⁡2(2)\frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(1 - \tan^{2}{\left(a \right)}\right) \cos^{4}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)} \tan{\left(\frac{a}{2} \right)}}{a \left(1 - \tan^{2}{\left(2 \right)}\right) \cos^{2}{\left(2 \right)}} 
   /     pi\
csc|-4 + --|
   \     2 /
------------
4*a*csc(4*a)
csc⁡(−4+π2)4acsc⁡(4a)\frac{\csc{\left(-4 + \frac{\pi}{2} \right)}}{4 a \csc{\left(4 a \right)}} 
     2       4/a\ /        2   \ /        2/a\\    /a\
2*sin (a)*sin |-|*\-1 + cot (a)/*|-1 + cot |-||*cot|-|
              \2/                \         \2//    \2/
------------------------------------------------------
                 /        2   \    2                  
               a*\-1 + cot (2)/*sin (2)
2(cot⁡2(a2)−1)(cot⁡2(a)−1)sin⁡4(a2)sin⁡2(a)cot⁡(a2)a(−1+cot⁡2(2))sin⁡2(2)\frac{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(a \right)} - 1\right) \sin^{4}{\left(\frac{a}{2} \right)} \sin^{2}{\left(a \right)} \cot{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(2 \right)}\right) \sin^{2}{\left(2 \right)}} 
                                                /          2/a\   \       
                            /          2      \ |       cos |-|   |       
     2/    pi\    3/a   pi\ |       cos (a)   | |           \2/   |    /a\
2*cos |a - --|*cos |- - --|*|-1 + ------------|*|-1 + ------------|*cos|-|
      \    2 /     \2   2 / |        2/    pi\| |        2/a   pi\|    \2/
                            |     cos |a - --|| |     cos |- - --||       
                            \         \    2 // \         \2   2 //       
--------------------------------------------------------------------------
                      /          2      \                                 
                      |       cos (2)   |    2/    pi\                    
                    a*|-1 + ------------|*cos |2 - --|                    
                      |        2/    pi\|     \    2 /                    
                      |     cos |2 - --||                                 
                      \         \    2 //
2(cos⁡2(a2)cos⁡2(a2−π2)−1)(cos⁡2(a)cos⁡2(a−π2)−1)cos⁡(a2)cos⁡3(a2−π2)cos⁡2(a−π2)a(−1+cos⁡2(2)cos⁡2(2−π2))cos⁡2(2−π2)\frac{2 \left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right) \left(\frac{\cos^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}} - 1\right) \cos{\left(\frac{a}{2} \right)} \cos^{3}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{a \left(-1 + \frac{\cos^{2}{\left(2 \right)}}{\cos^{2}{\left(2 - \frac{\pi}{2} \right)}}\right) \cos^{2}{\left(2 - \frac{\pi}{2} \right)}} 
    sin(4*a)   
---------------
       /    pi\
4*a*sin|4 + --|
       \    2 /
sin⁡(4a)4asin⁡(π2+4)\frac{\sin{\left(4 a \right)}}{4 a \sin{\left(\frac{\pi}{2} + 4 \right)}} 
                2                                             
   /       2   \     4/a\ /        1   \ /        1   \    /a\
32*\1 + tan (1)/ *tan |-|*|-1 + -------|*|-1 + -------|*tan|-|
                      \4/ |        2   | |        2/a\|    \2/
                          \     tan (a)/ |     tan |-||       
                                         \         \2//       
--------------------------------------------------------------
                   2              4                           
      /       2/a\\  /       2/a\\  /        1   \    2       
    a*|1 + tan |-|| *|1 + tan |-|| *|-1 + -------|*tan (1)    
      \        \2//  \        \4//  |        2   |            
                                    \     tan (2)/
32(−1+1tan⁡2(a2))(−1+1tan⁡2(a))(1+tan⁡2(1))2tan⁡4(a4)tan⁡(a2)a(−1+1tan⁡2(2))(tan⁡2(a4)+1)4(tan⁡2(a2)+1)2tan⁡2(1)\frac{32 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \tan^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} \right)}}{a \left(-1 + \frac{1}{\tan^{2}{\left(2 \right)}}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan^{2}{\left(1 \right)}} 
 sin(4*a) 
----------
4*a*cos(4)
sin⁡(4a)4acos⁡(4)\frac{\sin{\left(4 a \right)}}{4 a \cos{\left(4 \right)}} 
                               /         2    \
   3       2/a\ /        1   \ |      sin (a) |
sin (a)*sin |-|*|-1 + -------|*|-1 + ---------|
            \2/ |        2   | |          4/a\|
                \     tan (a)/ |     4*sin |-||
                               \           \2//
-----------------------------------------------
             /         2    \                  
             |      sin (4) |    2             
           a*|-1 + ---------|*sin (2)          
             |          4   |                  
             \     4*sin (2)/
(−1+sin⁡2(a)4sin⁡4(a2))(−1+1tan⁡2(a))sin⁡2(a2)sin⁡3(a)a(−1+sin⁡2(4)4sin⁡4(2))sin⁡2(2)\frac{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{3}{\left(a \right)}}{a \left(-1 + \frac{\sin^{2}{\left(4 \right)}}{4 \sin^{4}{\left(2 \right)}}\right) \sin^{2}{\left(2 \right)}} 
         sec(4)         
------------------------
a*csc(a)*sec(a)*sec(2*a)
sec⁡(4)acsc⁡(a)sec⁡(a)sec⁡(2a)\frac{\sec{\left(4 \right)}}{a \csc{\left(a \right)} \sec{\left(a \right)} \sec{\left(2 a \right)}} 
      /       2   \               
      \1 + cot (2)/*cot(2*a)      
----------------------------------
    /       2     \ /        2   \
2*a*\1 + cot (2*a)/*\-1 + cot (2)/
(cot⁡2(2)+1)cot⁡(2a)2a(−1+cot⁡2(2))(cot⁡2(2a)+1)\frac{\left(\cot^{2}{\left(2 \right)} + 1\right) \cot{\left(2 a \right)}}{2 a \left(-1 + \cot^{2}{\left(2 \right)}\right) \left(\cot^{2}{\left(2 a \right)} + 1\right)} 
                                    /         4/a\\                
                                    |    4*sin |-|| /         4   \
     2/a\    2/    pi\    4/pi   a\ |          \2/| |    4*sin (a)|
4*sin |-|*sin |a + --|*sin |-- + -|*|1 - ---------|*|1 - ---------|
      \2/     \    2 /     \2    2/ |        2    | |       2     |
                                    \     sin (a) / \    sin (2*a)/
-------------------------------------------------------------------
                 /         4   \                                   
                 |    4*sin (2)|           2/    pi\               
               a*|1 - ---------|*sin(a)*sin |2 + --|               
                 |        2    |            \    2 /               
                 \     sin (4) /
4(−4sin⁡4(a2)sin⁡2(a)+1)(−4sin⁡4(a)sin⁡2(2a)+1)sin⁡2(a2)sin⁡4(a2+π2)sin⁡2(a+π2)a(−4sin⁡4(2)sin⁡2(4)+1)sin⁡(a)sin⁡2(π2+2)\frac{4 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} \sin^{2}{\left(a + \frac{\pi}{2} \right)}}{a \left(- \frac{4 \sin^{4}{\left(2 \right)}}{\sin^{2}{\left(4 \right)}} + 1\right) \sin{\left(a \right)} \sin^{2}{\left(\frac{\pi}{2} + 2 \right)}} 
                   /    pi\
cos(a)*cos(2*a)*cos|a - --|
                   \    2 /
---------------------------
          a*cos(4)
cos⁡(a)cos⁡(2a)cos⁡(a−π2)acos⁡(4)\frac{\cos{\left(a \right)} \cos{\left(2 a \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{a \cos{\left(4 \right)}} 
                                        /         4/a\\
                                        |    4*sin |-||
     2       4/a\    2/a\ /       2   \ |          \2/|
4*cos (a)*cos |-|*sin |-|*\1 - tan (a)/*|1 - ---------|
              \2/     \2/               |        2    |
                                        \     sin (a) /
-------------------------------------------------------
              /         4   \                          
              |    4*sin (2)|    2                     
            a*|1 - ---------|*cos (2)*sin(a)           
              |        2    |                          
              \     sin (4) /
4(1−tan⁡2(a))(−4sin⁡4(a2)sin⁡2(a)+1)sin⁡2(a2)cos⁡4(a2)cos⁡2(a)a(−4sin⁡4(2)sin⁡2(4)+1)sin⁡(a)cos⁡2(2)\frac{4 \left(1 - \tan^{2}{\left(a \right)}\right) \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \cos^{4}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)}}{a \left(- \frac{4 \sin^{4}{\left(2 \right)}}{\sin^{2}{\left(4 \right)}} + 1\right) \sin{\left(a \right)} \cos^{2}{\left(2 \right)}} 
                /       2/pi    \\ /       2/pi   a\\ 
                |    csc |-- - a|| |    csc |-- - -|| 
     2/     pi\ |        \2     /| |        \2    2/| 
2*csc |-2 + --|*|1 - ------------|*|1 - ------------| 
      \     2 / |         2      | |         2/a\   | 
                \      csc (a)   / |      csc |-|   | 
                                   \          \2/   / 
------------------------------------------------------
  /       2/     pi\\                                 
  |    csc |-2 + --||                                 
  |        \     2 /|    /a\    2/pi    \    3/pi   a\
a*|1 - -------------|*csc|-|*csc |-- - a|*csc |-- - -|
  |          2      |    \2/     \2     /     \2    2/
  \       csc (2)   /
2(1−csc⁡2(−a2+π2)csc⁡2(a2))(1−csc⁡2(−a+π2)csc⁡2(a))csc⁡2(−2+π2)a(−csc⁡2(−2+π2)csc⁡2(2)+1)csc⁡(a2)csc⁡2(−a+π2)csc⁡3(−a2+π2)\frac{2 \left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 - \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}\right) \csc^{2}{\left(-2 + \frac{\pi}{2} \right)}}{a \left(- \frac{\csc^{2}{\left(-2 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 \right)}} + 1\right) \csc{\left(\frac{a}{2} \right)} \csc^{2}{\left(- a + \frac{\pi}{2} \right)} \csc^{3}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} 
                             /         2/a\   \ 
          /         2      \ |      sec |-|   | 
     2    |      sec (a)   | |          \2/   | 
2*sec (2)*|1 - ------------|*|1 - ------------| 
          |       2/    pi\| |       2/a   pi\| 
          |    sec |a - --|| |    sec |- - --|| 
          \        \    2 // \        \2   2 // 
------------------------------------------------
  /         2      \                            
  |      sec (2)   |    2       3/a\    /a   pi\
a*|1 - ------------|*sec (a)*sec |-|*sec|- - --|
  |       2/    pi\|             \2/    \2   2 /
  |    sec |2 - --||                            
  \        \    2 //
2(−sec⁡2(a2)sec⁡2(a2−π2)+1)(−sec⁡2(a)sec⁡2(a−π2)+1)sec⁡2(2)a(−sec⁡2(2)sec⁡2(2−π2)+1)sec⁡3(a2)sec⁡2(a)sec⁡(a2−π2)\frac{2 \left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \left(- \frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec^{2}{\left(2 \right)}}{a \left(- \frac{\sec^{2}{\left(2 \right)}}{\sec^{2}{\left(2 - \frac{\pi}{2} \right)}} + 1\right) \sec^{3}{\left(\frac{a}{2} \right)} \sec^{2}{\left(a \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} 
                2                                                                           
   /       2   \     4/a\    8/a\    4/a\ /       1   \ /        1   \ /        1   \    /a\
16*\1 + tan (1)/ *cos |-|*cos |-|*tan |-|*|-1 + ------|*|-1 + -------|*|-1 + -------|*tan|-|
                      \2/     \4/     \4/ \     cos(4)/ |        2   | |        2/a\|    \2/
                                                        \     tan (a)/ |     tan |-||       
                                                                       \         \2//       
--------------------------------------------------------------------------------------------
                                              2                                             
                                         a*tan (1)
16(−1+1tan⁡2(a2))(−1+1tan⁡2(a))(1+tan⁡2(1))2(1cos⁡(4)−1)cos⁡8(a4)cos⁡4(a2)tan⁡4(a4)tan⁡(a2)atan⁡2(1)\frac{16 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \left(\frac{1}{\cos{\left(4 \right)}} - 1\right) \cos^{8}{\left(\frac{a}{4} \right)} \cos^{4}{\left(\frac{a}{2} \right)} \tan^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} \right)}}{a \tan^{2}{\left(1 \right)}} 
      3/a\    4/a\    4/a\    8/a\    2    /        2   \ /        2/a\\
32*cot |-|*cot |-|*sin |-|*sin |-|*tan (1)*\-1 + cot (a)/*|-1 + cot |-||
       \2/     \4/     \2/     \4/                        \         \2//
------------------------------------------------------------------------
                          /        2   \    4                           
                        a*\-1 + cot (2)/*sin (1)
32(cot⁡2(a2)−1)(cot⁡2(a)−1)sin⁡8(a4)sin⁡4(a2)tan⁡2(1)cot⁡4(a4)cot⁡3(a2)a(−1+cot⁡2(2))sin⁡4(1)\frac{32 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(a \right)} - 1\right) \sin^{8}{\left(\frac{a}{4} \right)} \sin^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(1 \right)} \cot^{4}{\left(\frac{a}{4} \right)} \cot^{3}{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(2 \right)}\right) \sin^{4}{\left(1 \right)}} 
               2              3              4                                     
  /       2   \  /       2/a\\  /       2/a\\     4/a\    8/a\ /       2   \    /a\
2*\1 + tan (1)/ *|1 - tan |-|| *|1 - tan |-|| *cos |-|*cos |-|*\1 - tan (a)/*tan|-|
                 \        \2//  \        \4//      \2/     \4/                  \2/
-----------------------------------------------------------------------------------
                                          2                                        
                             /       2   \  /       2   \                          
                           a*\1 - tan (1)/ *\1 - tan (2)/
2(1+tan⁡2(1))2(1−tan⁡2(a4))4(1−tan⁡2(a2))3(1−tan⁡2(a))cos⁡8(a4)cos⁡4(a2)tan⁡(a2)a(1−tan⁡2(1))2(1−tan⁡2(2))\frac{2 \left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{3} \left(1 - \tan^{2}{\left(a \right)}\right) \cos^{8}{\left(\frac{a}{4} \right)} \cos^{4}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)}}{a \left(1 - \tan^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 \right)}\right)} 
               2               2               4                            
  /       2   \  /        2/a\\  /        2/a\\  /       1   \ /       1   \
2*\1 + cot (1)/ *|-1 + cot |-|| *|-1 + cot |-|| *|1 - -------|*|1 - -------|
                 \         \2//  \         \4//  |       2   | |       2/a\|
                                                 \    cot (a)/ |    cot |-||
                                                               \        \2//
----------------------------------------------------------------------------
                   2              4                             2           
      /       2/a\\  /       2/a\\  /       1   \ /        2   \     /a\    
    a*|1 + cot |-|| *|1 + cot |-|| *|1 - -------|*\-1 + cot (1)/ *cot|-|    
      \        \2//  \        \4//  |       2   |                    \2/    
                                    \    cot (2)/
2(1−1cot⁡2(a2))(1−1cot⁡2(a))(cot⁡2(1)+1)2(cot⁡2(a4)−1)4(cot⁡2(a2)−1)2a(−1+cot⁡2(1))2(1−1cot⁡2(2))(cot⁡2(a4)+1)4(cot⁡2(a2)+1)2cot⁡(a2)\frac{2 \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 - \frac{1}{\cot^{2}{\left(a \right)}}\right) \left(\cot^{2}{\left(1 \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{a \left(-1 + \cot^{2}{\left(1 \right)}\right)^{2} \left(1 - \frac{1}{\cot^{2}{\left(2 \right)}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot{\left(\frac{a}{2} \right)}} 
              /     pi\           
           csc|-4 + --|           
              \     2 /           
----------------------------------
            /pi    \    /pi      \
a*csc(a)*csc|-- - a|*csc|-- - 2*a|
            \2     /    \2       /
csc⁡(−4+π2)acsc⁡(a)csc⁡(−2a+π2)csc⁡(−a+π2)\frac{\csc{\left(-4 + \frac{\pi}{2} \right)}}{a \csc{\left(a \right)} \csc{\left(- 2 a + \frac{\pi}{2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}} 
      sec(4)     
-----------------
       /      pi\
4*a*sec|4*a - --|
       \      2 /
sec⁡(4)4asec⁡(4a−π2)\frac{\sec{\left(4 \right)}}{4 a \sec{\left(4 a - \frac{\pi}{2} \right)}} 
                              /          2/a\   \ 
          /          2      \ |       csc |-|   | 
     2    |       csc (a)   | |           \2/   | 
2*csc (2)*|-1 + ------------|*|-1 + ------------| 
          |        2/pi    \| |        2/pi   a\| 
          |     csc |-- - a|| |     csc |-- - -|| 
          \         \2     // \         \2    2// 
--------------------------------------------------
  /           2      \                            
  |        csc (2)   |    2       3/a\    /pi   a\
a*|-1 + -------------|*csc (a)*csc |-|*csc|-- - -|
  |        2/     pi\|             \2/    \2    2/
  |     csc |-2 + --||                            
  \         \     2 //
2(csc⁡2(a2)csc⁡2(−a2+π2)−1)(csc⁡2(a)csc⁡2(−a+π2)−1)csc⁡2(2)a(−1+csc⁡2(2)csc⁡2(−2+π2))csc⁡3(a2)csc⁡2(a)csc⁡(−a2+π2)\frac{2 \left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1\right) \left(\frac{\csc^{2}{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} - 1\right) \csc^{2}{\left(2 \right)}}{a \left(-1 + \frac{\csc^{2}{\left(2 \right)}}{\csc^{2}{\left(-2 + \frac{\pi}{2} \right)}}\right) \csc^{3}{\left(\frac{a}{2} \right)} \csc^{2}{\left(a \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} 
cos(a)*cos(2*a)*sin(a)
----------------------
       a*cos(4)
sin⁡(a)cos⁡(a)cos⁡(2a)acos⁡(4)\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}} 
               2              3              4                     
  /       2   \  /       2/a\\  /       2/a\\  /       2   \    /a\
2*\1 + tan (1)/ *|1 - tan |-|| *|1 - tan |-|| *\1 - tan (a)/*tan|-|
                 \        \2//  \        \4//                   \2/
-------------------------------------------------------------------
                   2              4              2                 
      /       2/a\\  /       2/a\\  /       2   \  /       2   \   
    a*|1 + tan |-|| *|1 + tan |-|| *\1 - tan (1)/ *\1 - tan (2)/   
      \        \2//  \        \4//
2(1+tan⁡2(1))2(1−tan⁡2(a4))4(1−tan⁡2(a2))3(1−tan⁡2(a))tan⁡(a2)a(1−tan⁡2(1))2(1−tan⁡2(2))(tan⁡2(a4)+1)4(tan⁡2(a2)+1)2\frac{2 \left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{3} \left(1 - \tan^{2}{\left(a \right)}\right) \tan{\left(\frac{a}{2} \right)}}{a \left(1 - \tan^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 \right)}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} 
                2                                              
   /       2   \     3/a\    4/a\ /        2   \ /        2/a\\
32*\1 + cot (1)/ *cot |-|*cot |-|*\-1 + cot (a)/*|-1 + cot |-||
                      \2/     \4/                \         \2//
---------------------------------------------------------------
                    2              4                           
       /       2/a\\  /       2/a\\  /        2   \    2       
     a*|1 + cot |-|| *|1 + cot |-|| *\-1 + cot (2)/*cot (1)    
       \        \2//  \        \4//
32(cot⁡2(1)+1)2(cot⁡2(a2)−1)(cot⁡2(a)−1)cot⁡4(a4)cot⁡3(a2)a(−1+cot⁡2(2))(cot⁡2(a4)+1)4(cot⁡2(a2)+1)2cot⁡2(1)\frac{32 \left(\cot^{2}{\left(1 \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(a \right)} - 1\right) \cot^{4}{\left(\frac{a}{4} \right)} \cot^{3}{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(2 \right)}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot^{2}{\left(1 \right)}} 
   2       2       3/a\ /       1   \ /        1   \ /        1   \    /a\
csc (2)*sin (a)*sin |-|*|-1 + ------|*|-1 + -------|*|-1 + -------|*cos|-|
                    \2/ \     cos(4)/ |        2   | |        2/a\|    \2/
                                      \     tan (a)/ |     tan |-||       
                                                     \         \2//       
--------------------------------------------------------------------------
                                    a
(−1+1tan⁡2(a2))(−1+1tan⁡2(a))(1cos⁡(4)−1)sin⁡3(a2)sin⁡2(a)cos⁡(a2)csc⁡2(2)a\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \left(\frac{1}{\cos{\left(4 \right)}} - 1\right) \sin^{3}{\left(\frac{a}{2} \right)} \sin^{2}{\left(a \right)} \cos{\left(\frac{a}{2} \right)} \csc^{2}{\left(2 \right)}}{a} 
  /       2   \ /        2   \ /        2/a\\    /a\
2*\1 + cot (2)/*\-1 + cot (a)/*|-1 + cot |-||*cot|-|
                               \         \2//    \2/
----------------------------------------------------
                                2                   
     /       2   \ /       2/a\\  /        2   \    
   a*\1 + cot (a)/*|1 + cot |-|| *\-1 + cot (2)/    
                   \        \2//
2(cot⁡2(2)+1)(cot⁡2(a2)−1)(cot⁡2(a)−1)cot⁡(a2)a(−1+cot⁡2(2))(cot⁡2(a2)+1)2(cot⁡2(a)+1)\frac{2 \left(\cot^{2}{\left(2 \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(a \right)} - 1\right) \cot{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(2 \right)}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(a \right)} + 1\right)} 
                2               4                                                   
  /        2/a\\  /        2/a\\     4/a\    8/a\ /       2   \ /       2/a\\    /a\
2*|-1 + cot |-|| *|-1 + cot |-|| *sin |-|*sin |-|*\1 - tan (a)/*|1 - tan |-||*tan|-|
  \         \2//  \         \4//      \2/     \4/               \        \2//    \2/
------------------------------------------------------------------------------------
                                                    2                               
                        /       2   \ /        2   \     4                          
                      a*\1 - tan (2)/*\-1 + cot (1)/ *sin (1)
2(1−tan⁡2(a2))(1−tan⁡2(a))(cot⁡2(a4)−1)4(cot⁡2(a2)−1)2sin⁡8(a4)sin⁡4(a2)tan⁡(a2)a(−1+cot⁡2(1))2(1−tan⁡2(2))sin⁡4(1)\frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(1 - \tan^{2}{\left(a \right)}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2} \sin^{8}{\left(\frac{a}{4} \right)} \sin^{4}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 \right)}\right) \sin^{4}{\left(1 \right)}} 
                /        2     \ /         2    \
   3       2/a\ |     sin (2*a)| |      sin (a) |
sin (a)*sin |-|*|-1 + ---------|*|-1 + ---------|
            \2/ |          4   | |          4/a\|
                \     4*sin (a)/ |     4*sin |-||
                                 \           \2//
-------------------------------------------------
              /         2    \                   
              |      sin (4) |    2              
            a*|-1 + ---------|*sin (2)           
              |          4   |                   
              \     4*sin (2)/
(−1+sin⁡2(a)4sin⁡4(a2))(−1+sin⁡2(2a)4sin⁡4(a))sin⁡2(a2)sin⁡3(a)a(−1+sin⁡2(4)4sin⁡4(2))sin⁡2(2)\frac{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{\sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{3}{\left(a \right)}}{a \left(-1 + \frac{\sin^{2}{\left(4 \right)}}{4 \sin^{4}{\left(2 \right)}}\right) \sin^{2}{\left(2 \right)}} 
     2       3/a\    2    /       2   \ /       2/a\\    /a\
2*cos (a)*cos |-|*sec (2)*\1 - tan (a)/*|1 - tan |-||*sin|-|
              \2/                       \        \2//    \2/
------------------------------------------------------------
                        /       2   \                       
                      a*\1 - tan (2)/
2(1−tan⁡2(a2))(1−tan⁡2(a))sin⁡(a2)cos⁡3(a2)cos⁡2(a)sec⁡2(2)a(1−tan⁡2(2))\frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(\frac{a}{2} \right)} \cos^{3}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)} \sec^{2}{\left(2 \right)}}{a \left(1 - \tan^{2}{\left(2 \right)}\right)} 
  /       2   \ /       2   \ /       2/a\\    /a\
2*\1 + tan (2)/*\1 - tan (a)/*|1 - tan |-||*tan|-|
                              \        \2//    \2/
--------------------------------------------------
                                2                 
     /       2   \ /       2/a\\  /       2   \   
   a*\1 + tan (a)/*|1 + tan |-|| *\1 - tan (2)/   
                   \        \2//
2(1+tan⁡2(2))(1−tan⁡2(a2))(1−tan⁡2(a))tan⁡(a2)a(1−tan⁡2(2))(tan⁡2(a2)+1)2(tan⁡2(a)+1)\frac{2 \left(1 + \tan^{2}{\left(2 \right)}\right) \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(1 - \tan^{2}{\left(a \right)}\right) \tan{\left(\frac{a}{2} \right)}}{a \left(1 - \tan^{2}{\left(2 \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\tan^{2}{\left(a \right)} + 1\right)} 
                  /       2/    pi\\ /       2/a   pi\\            
                  |    cos |a - --|| |    cos |- - --||            
     2       3/a\ |        \    2 /| |        \2   2 /|    /a   pi\
2*cos (a)*cos |-|*|1 - ------------|*|1 - ------------|*cos|- - --|
              \2/ |         2      | |         2/a\   |    \2   2 /
                  \      cos (a)   / |      cos |-|   |            
                                     \          \2/   /            
-------------------------------------------------------------------
                      /       2/    pi\\                           
                      |    cos |2 - --||                           
                      |        \    2 /|    2                      
                    a*|1 - ------------|*cos (2)                   
                      |         2      |                           
                      \      cos (2)   /
2(1−cos⁡2(a2−π2)cos⁡2(a2))(1−cos⁡2(a−π2)cos⁡2(a))cos⁡3(a2)cos⁡2(a)cos⁡(a2−π2)a(−cos⁡2(2−π2)cos⁡2(2)+1)cos⁡2(2)\frac{2 \left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 - \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}\right) \cos^{3}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{a \left(- \frac{\cos^{2}{\left(2 - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 \right)}} + 1\right) \cos^{2}{\left(2 \right)}} 
   /      pi\
cos|4*a - --|
   \      2 /
-------------
  4*a*cos(4)
cos⁡(4a−π2)4acos⁡(4)\frac{\cos{\left(4 a - \frac{\pi}{2} \right)}}{4 a \cos{\left(4 \right)}} 
     3       3/a\ /       2   \    /a\
4*cos (a)*cos |-|*\1 - tan (a)/*sin|-|
              \2/                  \2/
--------------------------------------
   /       2   \                 2    
 a*\1 - tan (2)/*(1 + cos(a))*cos (2)
4(1−tan⁡2(a))sin⁡(a2)cos⁡3(a2)cos⁡3(a)a(1−tan⁡2(2))(cos⁡(a)+1)cos⁡2(2)\frac{4 \left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(\frac{a}{2} \right)} \cos^{3}{\left(\frac{a}{2} \right)} \cos^{3}{\left(a \right)}}{a \left(1 - \tan^{2}{\left(2 \right)}\right) \left(\cos{\left(a \right)} + 1\right) \cos^{2}{\left(2 \right)}} 
sec(4)*sin(4*a)
---------------
      4*a
sin⁡(4a)sec⁡(4)4a\frac{\sin{\left(4 a \right)} \sec{\left(4 \right)}}{4 a} 
               /        2/    pi\\ /        2/a   pi\\
               |     sec |a - --|| |     sec |- - --||
     2/    pi\ |         \    2 /| |         \2   2 /|
2*sec |2 - --|*|-1 + ------------|*|-1 + ------------|
      \    2 / |          2      | |          2/a\   |
               \       sec (a)   / |       sec |-|   |
                                   \           \2/   /
------------------------------------------------------
  /        2/    pi\\                                 
  |     sec |2 - --||                                 
  |         \    2 /|    /a\    2/    pi\    3/a   pi\
a*|-1 + ------------|*sec|-|*sec |a - --|*sec |- - --|
  |          2      |    \2/     \    2 /     \2   2 /
  \       sec (2)   /
2(−1+sec⁡2(a2−π2)sec⁡2(a2))(−1+sec⁡2(a−π2)sec⁡2(a))sec⁡2(2−π2)a(−1+sec⁡2(2−π2)sec⁡2(2))sec⁡(a2)sec⁡3(a2−π2)sec⁡2(a−π2)\frac{2 \left(-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}}\right) \sec^{2}{\left(2 - \frac{\pi}{2} \right)}}{a \left(-1 + \frac{\sec^{2}{\left(2 - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 \right)}}\right) \sec{\left(\frac{a}{2} \right)} \sec^{3}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \sec^{2}{\left(a - \frac{\pi}{2} \right)}} 
      2       3/a\ /       1   \ /        1   \           /a\
-2*sin (a)*sin |-|*|-1 + ------|*|-1 + -------|*cos(a)*cos|-|
               \2/ \     cos(4)/ |        2   |           \2/
                                 \     tan (a)/              
-------------------------------------------------------------
                                      2                      
                   a*(-1 + cos(a))*sin (2)
−2(−1+1tan⁡2(a))(1cos⁡(4)−1)sin⁡3(a2)sin⁡2(a)cos⁡(a2)cos⁡(a)a(cos⁡(a)−1)sin⁡2(2)- \frac{2 \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \left(\frac{1}{\cos{\left(4 \right)}} - 1\right) \sin^{3}{\left(\frac{a}{2} \right)} \sin^{2}{\left(a \right)} \cos{\left(\frac{a}{2} \right)} \cos{\left(a \right)}}{a \left(\cos{\left(a \right)} - 1\right) \sin^{2}{\left(2 \right)}} 
          /    pi\    /pi      \
sin(a)*sin|a + --|*sin|-- + 2*a|
          \    2 /    \2       /
--------------------------------
              /    pi\          
         a*sin|4 + --|          
              \    2 /
sin⁡(a)sin⁡(a+π2)sin⁡(2a+π2)asin⁡(π2+4)\frac{\sin{\left(a \right)} \sin{\left(a + \frac{\pi}{2} \right)} \sin{\left(2 a + \frac{\pi}{2} \right)}}{a \sin{\left(\frac{\pi}{2} + 4 \right)}} 
            sec(4)           
-----------------------------
                     /    pi\
a*sec(a)*sec(2*a)*sec|a - --|
                     \    2 /
sec⁡(4)asec⁡(a)sec⁡(2a)sec⁡(a−π2)\frac{\sec{\left(4 \right)}}{a \sec{\left(a \right)} \sec{\left(2 a \right)} \sec{\left(a - \frac{\pi}{2} \right)}} 
      /       2   \              
      \1 + tan (2)/*tan(2*a)     
---------------------------------
    /       2     \ /       2   \
2*a*\1 + tan (2*a)/*\1 - tan (2)/
(1+tan⁡2(2))tan⁡(2a)2a(1−tan⁡2(2))(tan⁡2(2a)+1)\frac{\left(1 + \tan^{2}{\left(2 \right)}\right) \tan{\left(2 a \right)}}{2 a \left(1 - \tan^{2}{\left(2 \right)}\right) \left(\tan^{2}{\left(2 a \right)} + 1\right)} 
(1 + tan(2)^2)*tan(2*a)/(2*a*(1 + tan(2*a)^2)*(1 - tan(2)^2))
Potencias [src] 
cos(a)*cos(2*a)*sin(a)
----------------------
       a*cos(4)
sin⁡(a)cos⁡(a)cos⁡(2a)acos⁡(4)\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}} 
                    /   I*a    -I*a\ /   -2*I*a    2*I*a\ 
   /   -I*a    I*a\ |  e      e    | |  e         e     | 
-I*\- e     + e   /*|- ---- - -----|*|- ------- - ------| 
                    \   2       2  / \     2        2   / 
----------------------------------------------------------
                        / -4*I    4*I\                    
                        |e       e   |                    
                    2*a*|----- + ----|                    
                        \  2      2  /
−i(−eia2−e−ia2)(eia−e−ia)(−e2ia2−e−2ia2)2a(e4i2+e−4i2)- \frac{i \left(- \frac{e^{i a}}{2} - \frac{e^{- i a}}{2}\right) \left(e^{i a} - e^{- i a}\right) \left(- \frac{e^{2 i a}}{2} - \frac{e^{- 2 i a}}{2}\right)}{2 a \left(\frac{e^{4 i}}{2} + \frac{e^{- 4 i}}{2}\right)} 
-i*(-exp(-i*a) + exp(i*a))*(-exp(i*a)/2 - exp(-i*a)/2)*(-exp(-2*i*a)/2 - exp(2*i*a)/2)/(2*a*(exp(-4*i)/2 + exp(4*i)/2))
    © Sr Examen – Калькулятор