Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ cos(pi/(2-3*a))^2-(-cos(3*a))^2

¿Cómo vas a descomponer esta cos(pi/(2-3*a))^2-(-cos(3*a))^2 expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
   2/   pi  \              2
cos |-------| - (-cos(3*a)) 
    \2 - 3*a/
−(−cos⁡(3a))2+cos⁡2(π2−3a)- \left(- \cos{\left(3 a \right)}\right)^{2} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
cos(pi/(2 - 3*a))^2 - (-cos(3*a))^2
Simplificación general [src] 
   2/   pi   \      2     
cos |--------| - cos (3*a)
    \-2 + 3*a/
−cos⁡2(3a)+cos⁡2(π3a−2)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{3 a - 2} \right)} 
cos(pi/(-2 + 3*a))^2 - cos(3*a)^2
Respuesta numérica [src] 
cos(pi/(2 - 3*a))^2 - cos(3*a)^2
cos(pi/(2 - 3*a))^2 - cos(3*a)^2
Combinatoria [src] 
 /     /   pi  \           \ /              /   pi  \\
-|- cos|-------| + cos(3*a)|*|cos(3*a) + cos|-------||
 \     \2 - 3*a/           / \              \2 - 3*a//
−(cos⁡(3a)−cos⁡(π2−3a))(cos⁡(3a)+cos⁡(π2−3a))- \left(\cos{\left(3 a \right)} - \cos{\left(\frac{\pi}{2 - 3 a} \right)}\right) \left(\cos{\left(3 a \right)} + \cos{\left(\frac{\pi}{2 - 3 a} \right)}\right) 
-(-cos(pi/(2 - 3*a)) + cos(3*a))*(cos(3*a) + cos(pi/(2 - 3*a)))
Unión de expresiones racionales [src] 
   2/   pi  \      2     
cos |-------| - cos (3*a)
    \2 - 3*a/
−cos⁡2(3a)+cos⁡2(π2−3a)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
cos(pi/(2 - 3*a))^2 - cos(3*a)^2
Denominador común [src] 
   2/   pi  \      2     
cos |-------| - cos (3*a)
    \2 - 3*a/
−cos⁡2(3a)+cos⁡2(π2−3a)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
cos(pi/(2 - 3*a))^2 - cos(3*a)^2
Denominador racional [src] 
   2/   pi  \      2     
cos |-------| - cos (3*a)
    \2 - 3*a/
−cos⁡2(3a)+cos⁡2(π2−3a)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
cos(pi/(2 - 3*a))^2 - cos(3*a)^2
Potencias [src] 
                     2                        
/   pi*I      -pi*I \                         
| -------    -------|                        2
| 2 - 3*a    2 - 3*a|    /   -3*I*a    3*I*a\ 
|e          e       |    |  e         e     | 
|-------- + --------|  - |- ------- - ------| 
\   2          2    /    \     2        2   /
−(−e3ia2−e−3ia2)2+(eiπ2−3a2+e−iπ2−3a2)2- \left(- \frac{e^{3 i a}}{2} - \frac{e^{- 3 i a}}{2}\right)^{2} + \left(\frac{e^{\frac{i \pi}{2 - 3 a}}}{2} + \frac{e^{- \frac{i \pi}{2 - 3 a}}}{2}\right)^{2} 
   2/   pi  \      2     
cos |-------| - cos (3*a)
    \2 - 3*a/
−cos⁡2(3a)+cos⁡2(π2−3a)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
cos(pi/(2 - 3*a))^2 - cos(3*a)^2
Abrimos la expresión [src] 
   2/   pi  \      2     
cos |-------| - cos (3*a)
    \2 - 3*a/
−cos⁡2(3a)+cos⁡2(π2−3a)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
   2/   pi  \         6           2            4   
cos |-------| - 16*cos (a) - 9*cos (a) + 24*cos (a)
    \2 - 3*a/
−16cos⁡6(a)+24cos⁡4(a)−9cos⁡2(a)+cos⁡2(π2−3a)- 16 \cos^{6}{\left(a \right)} + 24 \cos^{4}{\left(a \right)} - 9 \cos^{2}{\left(a \right)} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
cos(pi/(2 - 3*a))^2 - 16*cos(a)^6 - 9*cos(a)^2 + 24*cos(a)^4
Compilar la expresión [src] 
   2/   pi  \      2     
cos |-------| - cos (3*a)
    \2 - 3*a/
−cos⁡2(3a)+cos⁡2(π2−3a)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
cos(pi/(2 - 3*a))^2 - cos(3*a)^2
Parte trigonométrica [src] 
      1                    1          
-------------- - ---------------------
   2/      pi\      2/  pi      pi   \
sec |3*a - --|   sec |- -- + --------|
    \      2 /       \  2    -2 + 3*a/
1sec⁡2(3a−π2)−1sec⁡2(−π2+π3a−2)\frac{1}{\sec^{2}{\left(3 a - \frac{\pi}{2} \right)}} - \frac{1}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{3 a - 2} \right)}} 
                                                     2
                        /          2/     pi    \   \ 
                        |       csc |-----------|   | 
                        |           \2*(2 - 3*a)/   | 
                        |-1 + ----------------------| 
                        |        2/pi        pi    \| 
                        |     csc |-- - -----------|| 
  1          1          \         \2    2*(2 - 3*a)// 
- - - --------------- + ------------------------------
  2        /pi      \              4/   pi   \        
      2*csc|-- - 6*a|           csc |--------|        
           \2       /               \-4 + 6*a/
(csc⁡2(π2(2−3a))csc⁡2(π2−π2(2−3a))−1)2csc⁡4(π6a−4)−12−12csc⁡(−6a+π2)\frac{\left(\frac{\csc^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)}}{\csc^{2}{\left(\frac{\pi}{2} - \frac{\pi}{2 \left(2 - 3 a\right)} \right)}} - 1\right)^{2}}{\csc^{4}{\left(\frac{\pi}{6 a - 4} \right)}} - \frac{1}{2} - \frac{1}{2 \csc{\left(- 6 a + \frac{\pi}{2} \right)}} 
          2/     pi     \            2/3*a\   
     4*tan |------------|       4*tan |---|   
           \2*(-2 + 3*a)/             \ 2 /   
- ------------------------- + ----------------
                          2                  2
  /       2/     pi     \\    /       2/3*a\\ 
  |1 + tan |------------||    |1 + tan |---|| 
  \        \2*(-2 + 3*a)//    \        \ 2 //
−4tan⁡2(π2(3a−2))(tan⁡2(π2(3a−2))+1)2+4tan⁡2(3a2)(tan⁡2(3a2)+1)2- \frac{4 \tan^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{3 a}{2} \right)}}{\left(\tan^{2}{\left(\frac{3 a}{2} \right)} + 1\right)^{2}} 
   2           2/   pi   \
sin (3*a) - sin |--------|
                \-2 + 3*a/
sin⁡2(3a)−sin⁡2(π3a−2)\sin^{2}{\left(3 a \right)} - \sin^{2}{\left(\frac{\pi}{3 a - 2} \right)} 
         1                  1       
------------------- - --------------
   2/pi      pi   \      2/pi      \
csc |-- - --------|   csc |-- - 3*a|
    \2    -2 + 3*a/       \2       /
−1csc⁡2(−3a+π2)+1csc⁡2(π2−π3a−2)- \frac{1}{\csc^{2}{\left(- 3 a + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(\frac{\pi}{2} - \frac{\pi}{3 a - 2} \right)}} 
                                                2                      
                 /           2/     pi    \    \                       
                 |        cos |-----------|    |                       
  1   cos(6*a)   |            \2*(2 - 3*a)/    |     4/  pi      pi   \
- - - -------- + |-1 + ------------------------| *cos |- -- + --------|
  2      2       |        2/  pi        pi    \|      \  2    -4 + 6*a/
                 |     cos |- -- + -----------||                       
                 \         \  2    2*(2 - 3*a)//
(cos⁡2(π2(2−3a))cos⁡2(−π2+π2(2−3a))−1)2cos⁡4(−π2+π6a−4)−cos⁡(6a)2−12\left(\frac{\cos^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{2 \left(2 - 3 a\right)} \right)}} - 1\right)^{2} \cos^{4}{\left(- \frac{\pi}{2} + \frac{\pi}{6 a - 4} \right)} - \frac{\cos{\left(6 a \right)}}{2} - \frac{1}{2} 
      1             1    
------------- - ---------
   2/   pi  \      2     
sec |-------|   sec (3*a)
    \2 - 3*a/
1sec⁡2(π2−3a)−1sec⁡2(3a)\frac{1}{\sec^{2}{\left(\frac{\pi}{2 - 3 a} \right)}} - \frac{1}{\sec^{2}{\left(3 a \right)}} 
   2/pi      pi  \      2/pi      \
sin |-- + -------| - sin |-- + 3*a|
    \2    2 - 3*a/       \2       /
sin⁡2(π2+π2−3a)−sin⁡2(3a+π2)\sin^{2}{\left(\frac{\pi}{2} + \frac{\pi}{2 - 3 a} \right)} - \sin^{2}{\left(3 a + \frac{\pi}{2} \right)} 
                                        2               
                 /         2/   pi  \  \                
                 |      sin |-------|  |                
  1   cos(6*a)   |          \2 - 3*a/  |     4/   pi   \
- - - -------- + |-1 + ----------------| *sin |--------|
  2      2       |          4/   pi   \|      \-4 + 6*a/
                 |     4*sin |--------||                
                 \           \-4 + 6*a//
(sin⁡2(π2−3a)4sin⁡4(π6a−4)−1)2sin⁡4(π6a−4)−cos⁡(6a)2−12\left(\frac{\sin^{2}{\left(\frac{\pi}{2 - 3 a} \right)}}{4 \sin^{4}{\left(\frac{\pi}{6 a - 4} \right)}} - 1\right)^{2} \sin^{4}{\left(\frac{\pi}{6 a - 4} \right)} - \frac{\cos{\left(6 a \right)}}{2} - \frac{1}{2} 
   2             2/   pi   \        4/   pi   \
sin (3*a) - 4*sin |--------| + 4*sin |--------|
                  \-4 + 6*a/         \-4 + 6*a/
sin⁡2(3a)+4sin⁡4(π6a−4)−4sin⁡2(π6a−4)\sin^{2}{\left(3 a \right)} + 4 \sin^{4}{\left(\frac{\pi}{6 a - 4} \right)} - 4 \sin^{2}{\left(\frac{\pi}{6 a - 4} \right)} 
          2/     pi     \            2/3*a\   
     4*cot |------------|       4*cot |---|   
           \2*(-2 + 3*a)/             \ 2 /   
- ------------------------- + ----------------
                          2                  2
  /       2/     pi     \\    /       2/3*a\\ 
  |1 + cot |------------||    |1 + cot |---|| 
  \        \2*(-2 + 3*a)//    \        \ 2 //
−4cot⁡2(π2(3a−2))(cot⁡2(π2(3a−2))+1)2+4cot⁡2(3a2)(cot⁡2(3a2)+1)2- \frac{4 \cot^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)}}{\left(\cot^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)} + 1\right)^{2}} + \frac{4 \cot^{2}{\left(\frac{3 a}{2} \right)}}{\left(\cot^{2}{\left(\frac{3 a}{2} \right)} + 1\right)^{2}} 
   2/   pi   \      2     
cos |--------| - cos (3*a)
    \-2 + 3*a/
−cos⁡2(3a)+cos⁡2(π3a−2)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{3 a - 2} \right)} 
   2/      pi\      2/  pi      pi   \
cos |3*a - --| - cos |- -- + --------|
    \      2 /       \  2    -2 + 3*a/
−cos⁡2(−π2+π3a−2)+cos⁡2(3a−π2)- \cos^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{3 a - 2} \right)} + \cos^{2}{\left(3 a - \frac{\pi}{2} \right)} 
    1             1       
--------- - --------------
   2           2/   pi   \
csc (3*a)   csc |--------|
                \-2 + 3*a/
−1csc⁡2(π3a−2)+1csc⁡2(3a)- \frac{1}{\csc^{2}{\left(\frac{\pi}{3 a - 2} \right)}} + \frac{1}{\csc^{2}{\left(3 a \right)}} 
                        2                  2
/       2/     pi     \\    /       2/3*a\\ 
|1 - tan |------------||    |1 - tan |---|| 
\        \2*(-2 + 3*a)//    \        \ 2 // 
------------------------- - ----------------
                        2                  2
/       2/     pi     \\    /       2/3*a\\ 
|1 + tan |------------||    |1 + tan |---|| 
\        \2*(-2 + 3*a)//    \        \ 2 //
−(1−tan⁡2(3a2))2(tan⁡2(3a2)+1)2+(1−tan⁡2(π2(3a−2)))2(tan⁡2(π2(3a−2))+1)2- \frac{\left(1 - \tan^{2}{\left(\frac{3 a}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{3 a}{2} \right)} + 1\right)^{2}} + \frac{\left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)} + 1\right)^{2}} 
                                          2               
  1 + cos(6*a)   /        2/     pi     \\     4/   pi   \
- ------------ + |-1 + cot |------------|| *sin |--------|
       2         \         \2*(-2 + 3*a)//      \-4 + 6*a/
−cos⁡(6a)+12+(cot⁡2(π2(3a−2))−1)2sin⁡4(π6a−4)- \frac{\cos{\left(6 a \right)} + 1}{2} + \left(\cot^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{\pi}{6 a - 4} \right)} 
                                                     2                   
                             /        2/     pi    \\     4/     pi     \
                2         16*|-1 + cot |-----------|| *cot |------------|
  1     -1 + cot (3*a)       \         \2*(2 - 3*a)//      \2*(-4 + 6*a)/
- - - ----------------- + -----------------------------------------------
  2     /       2     \                                      4           
      2*\1 + cot (3*a)/              /       2/     pi     \\            
                                     |1 + cot |------------||            
                                     \        \2*(-4 + 6*a)//
−cot⁡2(3a)−12(cot⁡2(3a)+1)+16(cot⁡2(π2(2−3a))−1)2cot⁡4(π2(6a−4))(cot⁡2(π2(6a−4))+1)4−12- \frac{\cot^{2}{\left(3 a \right)} - 1}{2 \left(\cot^{2}{\left(3 a \right)} + 1\right)} + \frac{16 \left(\cot^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)} - 1\right)^{2} \cot^{4}{\left(\frac{\pi}{2 \left(6 a - 4\right)} \right)}}{\left(\cot^{2}{\left(\frac{\pi}{2 \left(6 a - 4\right)} \right)} + 1\right)^{4}} - \frac{1}{2} 
                         2                   2
/        2/     pi     \\    /        2/3*a\\ 
|-1 + cot |------------||    |-1 + cot |---|| 
\         \2*(-2 + 3*a)//    \         \ 2 // 
-------------------------- - -----------------
                        2                    2
/       2/     pi     \\      /       2/3*a\\ 
|1 + cot |------------||      |1 + cot |---|| 
\        \2*(-2 + 3*a)//      \        \ 2 //
−(cot⁡2(3a2)−1)2(cot⁡2(3a2)+1)2+(cot⁡2(π2(3a−2))−1)2(cot⁡2(π2(3a−2))+1)2- \frac{\left(\cot^{2}{\left(\frac{3 a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{3 a}{2} \right)} + 1\right)^{2}} + \frac{\left(\cot^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{\pi}{2 \left(3 a - 2\right)} \right)} + 1\right)^{2}} 
                                                2               
         /pi      \   /           2/   pi  \   \                
      sin|-- + 6*a|   |        sin |-------|   |                
  1      \2       /   |            \2 - 3*a/   |     4/   pi   \
- - - ------------- + |-1 + -------------------| *sin |--------|
  2         2         |          4/     pi    \|      \-4 + 6*a/
                      |     4*sin |-----------||                
                      \           \2*(2 - 3*a)//
(−1+sin⁡2(π2−3a)4sin⁡4(π2(2−3a)))2sin⁡4(π6a−4)−sin⁡(6a+π2)2−12\left(-1 + \frac{\sin^{2}{\left(\frac{\pi}{2 - 3 a} \right)}}{4 \sin^{4}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)}}\right)^{2} \sin^{4}{\left(\frac{\pi}{6 a - 4} \right)} - \frac{\sin{\left(6 a + \frac{\pi}{2} \right)}}{2} - \frac{1}{2} 
                                         2               
  1 + cos(6*a)   /        2/     pi    \\     4/   pi   \
- ------------ + |-1 + cot |-----------|| *sin |--------|
       2         \         \2*(2 - 3*a)//      \-4 + 6*a/
−cos⁡(6a)+12+(cot⁡2(π2(2−3a))−1)2sin⁡4(π6a−4)- \frac{\cos{\left(6 a \right)} + 1}{2} + \left(\cot^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{\pi}{6 a - 4} \right)} 
   2/   pi  \      2     
cos |-------| - cos (3*a)
    \2 - 3*a/
−cos⁡2(3a)+cos⁡2(π2−3a)- \cos^{2}{\left(3 a \right)} + \cos^{2}{\left(\frac{\pi}{2 - 3 a} \right)} 
   2/pi      pi   \      2/pi      \
sin |-- + --------| - sin |-- + 3*a|
    \2    -2 + 3*a/       \2       /
sin⁡2(π2+π3a−2)−sin⁡2(3a+π2)\sin^{2}{\left(\frac{\pi}{2} + \frac{\pi}{3 a - 2} \right)} - \sin^{2}{\left(3 a + \frac{\pi}{2} \right)} 
      1              1    
-------------- - ---------
   2/   pi   \      2     
sec |--------|   sec (3*a)
    \-2 + 3*a/
1sec⁡2(π3a−2)−1sec⁡2(3a)\frac{1}{\sec^{2}{\left(\frac{\pi}{3 a - 2} \right)}} - \frac{1}{\sec^{2}{\left(3 a \right)}} 
        1                  1       
------------------ - --------------
   2/pi      pi  \      2/pi      \
csc |-- - -------|   csc |-- - 3*a|
    \2    2 - 3*a/       \2       /
−1csc⁡2(−3a+π2)+1csc⁡2(π2−π2−3a)- \frac{1}{\csc^{2}{\left(- 3 a + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(\frac{\pi}{2} - \frac{\pi}{2 - 3 a} \right)}} 
                                                  2
                   /        2/  pi        pi    \\ 
                   |     sec |- -- + -----------|| 
                   |         \  2    2*(2 - 3*a)/| 
                   |-1 + ------------------------| 
                   |           2/     pi    \    | 
                   |        sec |-----------|    | 
  1       1        \            \2*(2 - 3*a)/    / 
- - - ---------- + --------------------------------
  2   2*sec(6*a)           4/  pi      pi   \      
                        sec |- -- + --------|      
                            \  2    -4 + 6*a/
(−1+sec⁡2(−π2+π2(2−3a))sec⁡2(π2(2−3a)))2sec⁡4(−π2+π6a−4)−12−12sec⁡(6a)\frac{\left(-1 + \frac{\sec^{2}{\left(- \frac{\pi}{2} + \frac{\pi}{2 \left(2 - 3 a\right)} \right)}}{\sec^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)}}\right)^{2}}{\sec^{4}{\left(- \frac{\pi}{2} + \frac{\pi}{6 a - 4} \right)}} - \frac{1}{2} - \frac{1}{2 \sec{\left(6 a \right)}} 
                        2                   2
/        2/     pi    \\    /        2/3*a\\ 
|-1 + cot |-----------||    |-1 + cot |---|| 
\         \2*(2 - 3*a)//    \         \ 2 // 
------------------------- - -----------------
                        2                   2
 /       2/     pi    \\     /       2/3*a\\ 
 |1 + cot |-----------||     |1 + cot |---|| 
 \        \2*(2 - 3*a)//     \        \ 2 //
−(cot⁡2(3a2)−1)2(cot⁡2(3a2)+1)2+(cot⁡2(π2(2−3a))−1)2(cot⁡2(π2(2−3a))+1)2- \frac{\left(\cot^{2}{\left(\frac{3 a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{3 a}{2} \right)} + 1\right)^{2}} + \frac{\left(\cot^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)} + 1\right)^{2}} 
                                         2                                
  1   cos(6*a)      /           1       \     8/    pi   \    4/    pi   \
- - - -------- + 16*|-1 + --------------| *cos |---------|*tan |---------|
  2      2          |        2/   pi   \|      \-8 + 12*a/     \-8 + 12*a/
                    |     tan |--------||                                 
                    \         \-4 + 6*a//
16(−1+1tan⁡2(π6a−4))2cos⁡8(π12a−8)tan⁡4(π12a−8)−cos⁡(6a)2−1216 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{\pi}{6 a - 4} \right)}}\right)^{2} \cos^{8}{\left(\frac{\pi}{12 a - 8} \right)} \tan^{4}{\left(\frac{\pi}{12 a - 8} \right)} - \frac{\cos{\left(6 a \right)}}{2} - \frac{1}{2} 
                                                     2                   
                             /             1        \     4/     pi     \
                          16*|-1 + -----------------| *tan |------------|
                             |        2/     pi    \|      \2*(-4 + 6*a)/
               2             |     tan |-----------||                    
  1     1 - tan (3*a)        \         \2*(2 - 3*a)//                    
- - - ----------------- + -----------------------------------------------
  2     /       2     \                                      4           
      2*\1 + tan (3*a)/              /       2/     pi     \\            
                                     |1 + tan |------------||            
                                     \        \2*(-4 + 6*a)//
16(−1+1tan⁡2(π2(2−3a)))2tan⁡4(π2(6a−4))(tan⁡2(π2(6a−4))+1)4−1−tan⁡2(3a)2(tan⁡2(3a)+1)−12\frac{16 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)}}\right)^{2} \tan^{4}{\left(\frac{\pi}{2 \left(6 a - 4\right)} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(6 a - 4\right)} \right)} + 1\right)^{4}} - \frac{1 - \tan^{2}{\left(3 a \right)}}{2 \left(\tan^{2}{\left(3 a \right)} + 1\right)} - \frac{1}{2} 
                                            2                                   
  1   cos(6*a)      /        2/     pi    \\     4/     pi     \    8/    pi   \
- - - -------- + 16*|-1 + cot |-----------|| *cot |------------|*sin |---------|
  2      2          \         \2*(2 - 3*a)//      \2*(-4 + 6*a)/     \-8 + 12*a/
16(cot⁡2(π2(2−3a))−1)2sin⁡8(π12a−8)cot⁡4(π2(6a−4))−cos⁡(6a)2−1216 \left(\cot^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)} - 1\right)^{2} \sin^{8}{\left(\frac{\pi}{12 a - 8} \right)} \cot^{4}{\left(\frac{\pi}{2 \left(6 a - 4\right)} \right)} - \frac{\cos{\left(6 a \right)}}{2} - \frac{1}{2} 
                       2                  2
/       2/     pi    \\    /       2/3*a\\ 
|1 - tan |-----------||    |1 - tan |---|| 
\        \2*(2 - 3*a)//    \        \ 2 // 
------------------------ - ----------------
                       2                  2
/       2/     pi    \\    /       2/3*a\\ 
|1 + tan |-----------||    |1 + tan |---|| 
\        \2*(2 - 3*a)//    \        \ 2 //
−(1−tan⁡2(3a2))2(tan⁡2(3a2)+1)2+(1−tan⁡2(π2(2−3a)))2(tan⁡2(π2(2−3a))+1)2- \frac{\left(1 - \tan^{2}{\left(\frac{3 a}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{3 a}{2} \right)} + 1\right)^{2}} + \frac{\left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(2 - 3 a\right)} \right)} + 1\right)^{2}} 
(1 - tan(pi/(2*(2 - 3*a)))^2)^2/(1 + tan(pi/(2*(2 - 3*a)))^2)^2 - (1 - tan(3*a/2)^2)^2/(1 + tan(3*a/2)^2)^2
    © Sr Examen – Калькулятор