Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sin(4*x)/((cot(5*pi/4+2*x)*(1-sin(4*x))))

¿Cómo vas a descomponer esta sin(4*x)/((cot(5*pi/4+2*x)*(1-sin(4*x)))) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
           sin(4*x)           
------------------------------
   /5*pi      \               
cot|---- + 2*x|*(1 - sin(4*x))
   \ 4        /
sin⁡(4x)(1−sin⁡(4x))cot⁡(2x+5π4)\frac{\sin{\left(4 x \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \cot{\left(2 x + \frac{5 \pi}{4} \right)}} 
sin(4*x)/((cot((5*pi)/4 + 2*x)*(1 - sin(4*x))))
Simplificación general [src] 
             /      pi\ 
-sin(4*x)*tan|2*x + --| 
             \      4 / 
------------------------
     -1 + sin(4*x)
−sin⁡(4x)tan⁡(2x+π4)sin⁡(4x)−1- \frac{\sin{\left(4 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{\sin{\left(4 x \right)} - 1} 
-sin(4*x)*tan(2*x + pi/4)/(-1 + sin(4*x))
Respuesta numérica [src] 
sin(4*x)/((1.0 - sin(4*x))*cot((5*pi)/4 + 2*x))
sin(4*x)/((1.0 - sin(4*x))*cot((5*pi)/4 + 2*x))
Potencias [src] 
             /   -4*I*x    4*I*x\           
          -I*\- e       + e     /           
--------------------------------------------
  /      /   -4*I*x    4*I*x\\              
  |    I*\- e       + e     /|    /      pi\
2*|1 + ----------------------|*cot|2*x + --|
  \              2           /    \      4 /
−i(e4ix−e−4ix)2(i(e4ix−e−4ix)2+1)cot⁡(2x+π4)- \frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{2 \left(\frac{i \left(e^{4 i x} - e^{- 4 i x}\right)}{2} + 1\right) \cot{\left(2 x + \frac{\pi}{4} \right)}} 
          sin(4*x)          
----------------------------
                  /      pi\
(1 - sin(4*x))*cot|2*x + --|
                  \      4 /
sin⁡(4x)(1−sin⁡(4x))cot⁡(2x+π4)\frac{\sin{\left(4 x \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \cot{\left(2 x + \frac{\pi}{4} \right)}} 
sin(4*x)/((1 - sin(4*x))*cot(2*x + pi/4))
Denominador común [src] 
               -sin(4*x)                
----------------------------------------
     /      pi\      /      pi\         
- cot|2*x + --| + cot|2*x + --|*sin(4*x)
     \      4 /      \      4 /
−sin⁡(4x)sin⁡(4x)cot⁡(2x+π4)−cot⁡(2x+π4)- \frac{\sin{\left(4 x \right)}}{\sin{\left(4 x \right)} \cot{\left(2 x + \frac{\pi}{4} \right)} - \cot{\left(2 x + \frac{\pi}{4} \right)}} 
-sin(4*x)/(-cot(2*x + pi/4) + cot(2*x + pi/4)*sin(4*x))
Unión de expresiones racionales [src] 
           sin(4*x)           
------------------------------
                  /5*pi + 8*x\
(1 - sin(4*x))*cot|----------|
                  \    4     /
sin⁡(4x)(1−sin⁡(4x))cot⁡(8x+5π4)\frac{\sin{\left(4 x \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \cot{\left(\frac{8 x + 5 \pi}{4} \right)}} 
sin(4*x)/((1 - sin(4*x))*cot((5*pi + 8*x)/4))
Combinatoria [src] 
          -sin(4*x)          
-----------------------------
                   /      pi\
(-1 + sin(4*x))*cot|2*x + --|
                   \      4 /
−sin⁡(4x)(sin⁡(4x)−1)cot⁡(2x+π4)- \frac{\sin{\left(4 x \right)}}{\left(\sin{\left(4 x \right)} - 1\right) \cot{\left(2 x + \frac{\pi}{4} \right)}} 
-sin(4*x)/((-1 + sin(4*x))*cot(2*x + pi/4))
Abrimos la expresión [src] 
                                                                                                                3                                                                                                                                                                                                                                                                                                                                                        
                                                                                                           8*sin (x)*cos(x)                                                                                                                                                                                                                     4*cos(x)*sin(x)                                                                                                          
- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                          3                       3                                                                                               3                                                                                                            3                       3                                                                                               3                 
              1                        1                        cot(x)               8*sin (x)*cos(x)        4*sin (x)*cos(x)         2*cos(x)*sin(x)          4*cos(x)*sin(x)      2*cos(x)*cot(x)*sin(x)   4*sin (x)*cos(x)*cot(x)               1                        1                        cot(x)               8*sin (x)*cos(x)        4*sin (x)*cos(x)         2*cos(x)*sin(x)          4*cos(x)*sin(x)      2*cos(x)*cot(x)*sin(x)   4*sin (x)*cos(x)*cot(x)
  - --------------------- - ----------------------- + ------------------------- - --------------------- - ---------------------- + ---------------------- + --------------------- - ---------------------- + -----------------------   - --------------------- - ----------------------- + ------------------------- - --------------------- - ---------------------- + ---------------------- + --------------------- - ---------------------- + -----------------------
        cot(x)      1               2                   /    cot(x)      1    \       cot(x)      1                2                        2                   cot(x)      1           cot(x)      1             cot(x)      1              cot(x)      1               2                   /    cot(x)      1    \       cot(x)      1                2                        2                   cot(x)      1           cot(x)      1             cot(x)      1     
    1 + ------ - --------   -1 + cot (x) + 2*cot(x)   2*|1 + ------ - --------|   1 + ------ - --------     1   cot (x)              1   cot (x)            1 + ------ - --------   1 + ------ - --------     1 + ------ - --------      1 + ------ - --------   -1 + cot (x) + 2*cot(x)   2*|1 + ------ - --------|   1 + ------ - --------     1   cot (x)              1   cot (x)            1 + ------ - --------   1 + ------ - --------     1 + ------ - -------- 
          2      2*cot(x)                               \      2      2*cot(x)/         2      2*cot(x)   - - + ------- + cot(x)   - - + ------- + cot(x)         2      2*cot(x)         2      2*cot(x)           2      2*cot(x)            2      2*cot(x)                               \      2      2*cot(x)/         2      2*cot(x)   - - + ------- + cot(x)   - - + ------- + cot(x)         2      2*cot(x)         2      2*cot(x)           2      2*cot(x) 
                                                                                                            2      2                 2      2                                                                                                                                                                                                    2      2                 2      2
−8sin⁡3(x)cos⁡(x)−1cot⁡2(x)+2cot⁡(x)−1−4sin⁡3(x)cos⁡(x)cot⁡2(x)2+cot⁡(x)−12+2sin⁡(x)cos⁡(x)cot⁡2(x)2+cot⁡(x)−12+4sin⁡3(x)cos⁡(x)cot⁡(x)cot⁡(x)2+1−12cot⁡(x)−8sin⁡3(x)cos⁡(x)cot⁡(x)2+1−12cot⁡(x)−2sin⁡(x)cos⁡(x)cot⁡(x)cot⁡(x)2+1−12cot⁡(x)+4sin⁡(x)cos⁡(x)cot⁡(x)2+1−12cot⁡(x)+cot⁡(x)2(cot⁡(x)2+1−12cot⁡(x))−1cot⁡(x)2+1−12cot⁡(x)+4sin⁡(x)cos⁡(x)−1cot⁡2(x)+2cot⁡(x)−1−4sin⁡3(x)cos⁡(x)cot⁡2(x)2+cot⁡(x)−12+2sin⁡(x)cos⁡(x)cot⁡2(x)2+cot⁡(x)−12+4sin⁡3(x)cos⁡(x)cot⁡(x)cot⁡(x)2+1−12cot⁡(x)−8sin⁡3(x)cos⁡(x)cot⁡(x)2+1−12cot⁡(x)−2sin⁡(x)cos⁡(x)cot⁡(x)cot⁡(x)2+1−12cot⁡(x)+4sin⁡(x)cos⁡(x)cot⁡(x)2+1−12cot⁡(x)+cot⁡(x)2(cot⁡(x)2+1−12cot⁡(x))−1cot⁡(x)2+1−12cot⁡(x)- \frac{8 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{- \frac{1}{\cot^{2}{\left(x \right)} + 2 \cot{\left(x \right)} - 1} - \frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{\frac{\cot^{2}{\left(x \right)}}{2} + \cot{\left(x \right)} - \frac{1}{2}} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\frac{\cot^{2}{\left(x \right)}}{2} + \cot{\left(x \right)} - \frac{1}{2}} + \frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)} \cot{\left(x \right)}}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}} - \frac{8 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}} - \frac{2 \sin{\left(x \right)} \cos{\left(x \right)} \cot{\left(x \right)}}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}} + \frac{\cot{\left(x \right)}}{2 \left(\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}\right)} - \frac{1}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}}} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{- \frac{1}{\cot^{2}{\left(x \right)} + 2 \cot{\left(x \right)} - 1} - \frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{\frac{\cot^{2}{\left(x \right)}}{2} + \cot{\left(x \right)} - \frac{1}{2}} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\frac{\cot^{2}{\left(x \right)}}{2} + \cot{\left(x \right)} - \frac{1}{2}} + \frac{4 \sin^{3}{\left(x \right)} \cos{\left(x \right)} \cot{\left(x \right)}}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}} - \frac{8 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}} - \frac{2 \sin{\left(x \right)} \cos{\left(x \right)} \cot{\left(x \right)}}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)}}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}} + \frac{\cot{\left(x \right)}}{2 \left(\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}\right)} - \frac{1}{\frac{\cot{\left(x \right)}}{2} + 1 - \frac{1}{2 \cot{\left(x \right)}}}} 
-8*sin(x)^3*cos(x)/(-1/(1 + cot(x)/2 - 1/(2*cot(x))) - 1/(-1 + cot(x)^2 + 2*cot(x)) + cot(x)/(2*(1 + cot(x)/2 - 1/(2*cot(x)))) - 8*sin(x)^3*cos(x)/(1 + cot(x)/2 - 1/(2*cot(x))) - 4*sin(x)^3*cos(x)/(-1/2 + cot(x)^2/2 + cot(x)) + 2*cos(x)*sin(x)/(-1/2 + cot(x)^2/2 + cot(x)) + 4*cos(x)*sin(x)/(1 + cot(x)/2 - 1/(2*cot(x))) - 2*cos(x)*cot(x)*sin(x)/(1 + cot(x)/2 - 1/(2*cot(x))) + 4*sin(x)^3*cos(x)*cot(x)/(1 + cot(x)/2 - 1/(2*cot(x)))) + 4*cos(x)*sin(x)/(-1/(1 + cot(x)/2 - 1/(2*cot(x))) - 1/(-1 + cot(x)^2 + 2*cot(x)) + cot(x)/(2*(1 + cot(x)/2 - 1/(2*cot(x)))) - 8*sin(x)^3*cos(x)/(1 + cot(x)/2 - 1/(2*cot(x))) - 4*sin(x)^3*cos(x)/(-1/2 + cot(x)^2/2 + cot(x)) + 2*cos(x)*sin(x)/(-1/2 + cot(x)^2/2 + cot(x)) + 4*cos(x)*sin(x)/(1 + cot(x)/2 - 1/(2*cot(x))) - 2*cos(x)*cot(x)*sin(x)/(1 + cot(x)/2 - 1/(2*cot(x))) + 4*sin(x)^3*cos(x)*cot(x)/(1 + cot(x)/2 - 1/(2*cot(x))))
Denominador racional [src] 
          -sin(4*x)          
-----------------------------
                   /      pi\
(-1 + sin(4*x))*cot|2*x + --|
                   \      4 /
−sin⁡(4x)(sin⁡(4x)−1)cot⁡(2x+π4)- \frac{\sin{\left(4 x \right)}}{\left(\sin{\left(4 x \right)} - 1\right) \cot{\left(2 x + \frac{\pi}{4} \right)}} 
-sin(4*x)/((-1 + sin(4*x))*cot(2*x + pi/4))
Parte trigonométrica [src] 
                    2                           
               8*cot (x)*cot(2*x)               
------------------------------------------------
             2                                  
/       2   \  /      2*cot(2*x) \    /      pi\
\1 + cot (x)/ *|1 - -------------|*cot|2*x + --|
               |           2     |    \      4 /
               \    1 + cot (2*x)/
8cot⁡2(x)cot⁡(2x)(1−2cot⁡(2x)cot⁡2(2x)+1)(cot⁡2(x)+1)2cot⁡(2x+π4)\frac{8 \cot^{2}{\left(x \right)} \cot{\left(2 x \right)}}{\left(1 - \frac{2 \cot{\left(2 x \right)}}{\cot^{2}{\left(2 x \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(2 x + \frac{\pi}{4} \right)}} 
                2                               
  /        2   \     4                /      pi\
2*\-1 + cot (x)/ *sin (x)*tan(2*x)*tan|2*x + --|
                                      \      4 /
------------------------------------------------
                  1 - sin(4*x)
2(cot⁡2(x)−1)2sin⁡4(x)tan⁡(2x)tan⁡(2x+π4)1−sin⁡(4x)\frac{2 \left(\cot^{2}{\left(x \right)} - 1\right)^{2} \sin^{4}{\left(x \right)} \tan{\left(2 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{1 - \sin{\left(4 x \right)}} 
     2/      pi\         
2*cos |2*x - --|*sin(4*x)
      \      4 /         
-------------------------
 (1 - sin(4*x))*cos(4*x)
2sin⁡(4x)cos⁡2(2x−π4)(1−sin⁡(4x))cos⁡(4x)\frac{2 \sin{\left(4 x \right)} \cos^{2}{\left(2 x - \frac{\pi}{4} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \cos{\left(4 x \right)}} 
                                    2                    
                      /        2   \                     
                    2*\-1 + cot (x)/                     
---------------------------------------------------------
             2                                           
/       2   \  /      2*cot(2*x) \             /      pi\
\1 + cot (x)/ *|1 - -------------|*cot(2*x)*cot|2*x + --|
               |           2     |             \      4 /
               \    1 + cot (2*x)/
2(cot⁡2(x)−1)2(1−2cot⁡(2x)cot⁡2(2x)+1)(cot⁡2(x)+1)2cot⁡(2x)cot⁡(2x+π4)\frac{2 \left(\cot^{2}{\left(x \right)} - 1\right)^{2}}{\left(1 - \frac{2 \cot{\left(2 x \right)}}{\cot^{2}{\left(2 x \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(2 x \right)} \cot{\left(2 x + \frac{\pi}{4} \right)}} 
      /      pi\    /      pi\   
   cos|2*x - --|*cos|4*x - --|   
      \      4 /    \      2 /   
---------------------------------
/       /      pi\\    /      pi\
|1 - cos|4*x - --||*cos|2*x + --|
\       \      2 //    \      4 /
cos⁡(2x−π4)cos⁡(4x−π2)(1−cos⁡(4x−π2))cos⁡(2x+π4)\frac{\cos{\left(2 x - \frac{\pi}{4} \right)} \cos{\left(4 x - \frac{\pi}{2} \right)}}{\left(1 - \cos{\left(4 x - \frac{\pi}{2} \right)}\right) \cos{\left(2 x + \frac{\pi}{4} \right)}} 
               /      pi\            
            sec|2*x + --|            
               \      4 /            
-------------------------------------
/       1    \             /      pi\
|1 - --------|*csc(4*x)*csc|2*x + --|
\    csc(4*x)/             \      4 /
sec⁡(2x+π4)(1−1csc⁡(4x))csc⁡(4x)csc⁡(2x+π4)\frac{\sec{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \frac{1}{\csc{\left(4 x \right)}}\right) \csc{\left(4 x \right)} \csc{\left(2 x + \frac{\pi}{4} \right)}} 
                      2/    pi\                         
                16*cot |x + --|*cot(2*x)                
                       \    8 /                         
--------------------------------------------------------
                  2                                     
/       2/    pi\\  /      2*cot(2*x) \ /        2     \
|1 + cot |x + --|| *|1 - -------------|*\-1 + cot (2*x)/
\        \    8 //  |           2     |                 
                    \    1 + cot (2*x)/
16cot⁡(2x)cot⁡2(x+π8)(1−2cot⁡(2x)cot⁡2(2x)+1)(cot⁡2(2x)−1)(cot⁡2(x+π8)+1)2\frac{16 \cot{\left(2 x \right)} \cot^{2}{\left(x + \frac{\pi}{8} \right)}}{\left(1 - \frac{2 \cot{\left(2 x \right)}}{\cot^{2}{\left(2 x \right)} + 1}\right) \left(\cot^{2}{\left(2 x \right)} - 1\right) \left(\cot^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right)^{2}} 
                         /      pi\                     
                    2*sec|2*x + --|                     
                         \      4 /                     
--------------------------------------------------------
/          1      \             /      pi\    /      pi\
|1 - -------------|*sec(2*x)*sec|2*x - --|*sec|2*x - --|
|       /      pi\|             \      2 /    \      4 /
|    sec|4*x - --||                                     
\       \      2 //
2sec⁡(2x+π4)(1−1sec⁡(4x−π2))sec⁡(2x)sec⁡(2x−π2)sec⁡(2x−π4)\frac{2 \sec{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \frac{1}{\sec{\left(4 x - \frac{\pi}{2} \right)}}\right) \sec{\left(2 x \right)} \sec{\left(2 x - \frac{\pi}{2} \right)} \sec{\left(2 x - \frac{\pi}{4} \right)}} 
               /      pi\   
   sin(4*x)*sin|2*x + --|   
               \      4 /   
----------------------------
                  /      pi\
(1 - sin(4*x))*cos|2*x + --|
                  \      4 /
sin⁡(4x)sin⁡(2x+π4)(1−sin⁡(4x))cos⁡(2x+π4)\frac{\sin{\left(4 x \right)} \sin{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \cos{\left(2 x + \frac{\pi}{4} \right)}} 
     2                  /      pi\
2*sin (2*x)*cot(2*x)*tan|2*x + --|
                        \      4 /
----------------------------------
           1 - sin(4*x)
2sin⁡2(2x)tan⁡(2x+π4)cot⁡(2x)1−sin⁡(4x)\frac{2 \sin^{2}{\left(2 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)} \cot{\left(2 x \right)}}{1 - \sin{\left(4 x \right)}} 
      2/    pi\    4/    pi\         
16*cot |x + --|*sin |x + --|*cot(2*x)
       \    8 /     \    8 /         
-------------------------------------
                  /        2     \   
   (1 - sin(4*x))*\-1 + cot (2*x)/
16sin⁡4(x+π8)cot⁡(2x)cot⁡2(x+π8)(1−sin⁡(4x))(cot⁡2(2x)−1)\frac{16 \sin^{4}{\left(x + \frac{\pi}{8} \right)} \cot{\left(2 x \right)} \cot^{2}{\left(x + \frac{\pi}{8} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \left(\cot^{2}{\left(2 x \right)} - 1\right)} 
     2         2/pi      \    2/      pi\
8*sin (2*x)*sin |-- + 2*x|*sin |2*x + --|
                \2       /     \      4 /
-----------------------------------------
     (1 - sin(4*x))*cos(4*x)*sin(4*x)
8sin⁡2(2x)sin⁡2(2x+π4)sin⁡2(2x+π2)(1−sin⁡(4x))sin⁡(4x)cos⁡(4x)\frac{8 \sin^{2}{\left(2 x \right)} \sin^{2}{\left(2 x + \frac{\pi}{4} \right)} \sin^{2}{\left(2 x + \frac{\pi}{2} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \sin{\left(4 x \right)} \cos{\left(4 x \right)}} 
     2                  /      pi\
2*cos (2*x)*tan(2*x)*tan|2*x + --|
                        \      4 /
----------------------------------
           1 - sin(4*x)
2cos⁡2(2x)tan⁡(2x)tan⁡(2x+π4)1−sin⁡(4x)\frac{2 \cos^{2}{\left(2 x \right)} \tan{\left(2 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{1 - \sin{\left(4 x \right)}} 
                /pi      \            
           2*csc|-- - 4*x|            
                \2       /            
--------------------------------------
/       1    \             2/      pi\
|1 - --------|*csc(4*x)*csc |2*x + --|
\    csc(4*x)/              \      4 /
2csc⁡(−4x+π2)(1−1csc⁡(4x))csc⁡(4x)csc⁡2(2x+π4)\frac{2 \csc{\left(- 4 x + \frac{\pi}{2} \right)}}{\left(1 - \frac{1}{\csc{\left(4 x \right)}}\right) \csc{\left(4 x \right)} \csc^{2}{\left(2 x + \frac{\pi}{4} \right)}} 
     4       2       /      pi\
8*cos (x)*tan (x)*tan|2*x + --|
                     \      4 /
-------------------------------
    (1 - sin(4*x))*tan(2*x)
8cos⁡4(x)tan⁡2(x)tan⁡(2x+π4)(1−sin⁡(4x))tan⁡(2x)\frac{8 \cos^{4}{\left(x \right)} \tan^{2}{\left(x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \tan{\left(2 x \right)}} 
                   2*sec(4*x)                   
------------------------------------------------
/          1      \    2/      pi\    /      pi\
|1 - -------------|*sec |2*x - --|*sec|4*x - --|
|       /      pi\|     \      4 /    \      2 /
|    sec|4*x - --||                             
\       \      2 //
2sec⁡(4x)(1−1sec⁡(4x−π2))sec⁡2(2x−π4)sec⁡(4x−π2)\frac{2 \sec{\left(4 x \right)}}{\left(1 - \frac{1}{\sec{\left(4 x - \frac{\pi}{2} \right)}}\right) \sec^{2}{\left(2 x - \frac{\pi}{4} \right)} \sec{\left(4 x - \frac{\pi}{2} \right)}} 
                    /      pi\     
      2*tan(2*x)*tan|2*x + --|     
                    \      4 /     
-----------------------------------
/       2     \ /      2*tan(2*x) \
\1 + tan (2*x)/*|1 - -------------|
                |           2     |
                \    1 + tan (2*x)/
2tan⁡(2x)tan⁡(2x+π4)(1−2tan⁡(2x)tan⁡2(2x)+1)(tan⁡2(2x)+1)\frac{2 \tan{\left(2 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \frac{2 \tan{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)} + 1}\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)} 
                      2/    pi\                        
                16*tan |x + --|*tan(2*x)               
                       \    8 /                        
-------------------------------------------------------
                  2                                    
/       2/    pi\\  /       2     \ /      2*tan(2*x) \
|1 + tan |x + --|| *\1 - tan (2*x)/*|1 - -------------|
\        \    8 //                  |           2     |
                                    \    1 + tan (2*x)/
16tan⁡(2x)tan⁡2(x+π8)(1−2tan⁡(2x)tan⁡2(2x)+1)(1−tan⁡2(2x))(tan⁡2(x+π8)+1)2\frac{16 \tan{\left(2 x \right)} \tan^{2}{\left(x + \frac{\pi}{8} \right)}}{\left(1 - \frac{2 \tan{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)} + 1}\right) \left(1 - \tan^{2}{\left(2 x \right)}\right) \left(\tan^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right)^{2}} 
                    2*cot(2*x)                   
-------------------------------------------------
/       2     \ /      2*cot(2*x) \    /      pi\
\1 + cot (2*x)/*|1 - -------------|*cot|2*x + --|
                |           2     |    \      4 /
                \    1 + cot (2*x)/
2cot⁡(2x)(1−2cot⁡(2x)cot⁡2(2x)+1)(cot⁡2(2x)+1)cot⁡(2x+π4)\frac{2 \cot{\left(2 x \right)}}{\left(1 - \frac{2 \cot{\left(2 x \right)}}{\cot^{2}{\left(2 x \right)} + 1}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right) \cot{\left(2 x + \frac{\pi}{4} \right)}} 
      2/      pi\           
 2*sin |2*x + --|*sin(4*x)  
       \      4 /           
----------------------------
                  /pi      \
(1 - sin(4*x))*sin|-- + 4*x|
                  \2       /
2sin⁡(4x)sin⁡2(2x+π4)(1−sin⁡(4x))sin⁡(4x+π2)\frac{2 \sin{\left(4 x \right)} \sin^{2}{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \sin{\left(4 x + \frac{\pi}{2} \right)}} 
               2                       
  /       2   \              /      pi\
2*\1 - tan (x)/ *tan(2*x)*tan|2*x + --|
                             \      4 /
---------------------------------------
                2                      
   /       2   \  /      2*tan(2*x) \  
   \1 + tan (x)/ *|1 - -------------|  
                  |           2     |  
                  \    1 + tan (2*x)/
2(1−tan⁡2(x))2tan⁡(2x)tan⁡(2x+π4)(1−2tan⁡(2x)tan⁡2(2x)+1)(tan⁡2(x)+1)2\frac{2 \left(1 - \tan^{2}{\left(x \right)}\right)^{2} \tan{\left(2 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \frac{2 \tan{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}} 
              /      pi\    /      pi\
2*cos(2*x)*cos|2*x - --|*cos|2*x - --|
              \      2 /    \      4 /
--------------------------------------
  /       /      pi\\    /      pi\   
  |1 - cos|4*x - --||*cos|2*x + --|   
  \       \      2 //    \      4 /
2cos⁡(2x)cos⁡(2x−π2)cos⁡(2x−π4)(1−cos⁡(4x−π2))cos⁡(2x+π4)\frac{2 \cos{\left(2 x \right)} \cos{\left(2 x - \frac{\pi}{2} \right)} \cos{\left(2 x - \frac{\pi}{4} \right)}}{\left(1 - \cos{\left(4 x - \frac{\pi}{2} \right)}\right) \cos{\left(2 x + \frac{\pi}{4} \right)}} 
        /pi      \           
   2*csc|-- - 4*x|*sin(4*x)  
        \2       /           
-----------------------------
                  2/      pi\
(1 - sin(4*x))*csc |2*x + --|
                   \      4 /
2sin⁡(4x)csc⁡(−4x+π2)(1−sin⁡(4x))csc⁡2(2x+π4)\frac{2 \sin{\left(4 x \right)} \csc{\left(- 4 x + \frac{\pi}{2} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \csc^{2}{\left(2 x + \frac{\pi}{4} \right)}} 
                    /      pi\                 
                 sec|2*x + --|                 
                    \      4 /                 
-----------------------------------------------
/          1      \    /      pi\    /      pi\
|1 - -------------|*sec|2*x - --|*sec|4*x - --|
|       /      pi\|    \      4 /    \      2 /
|    sec|4*x - --||                            
\       \      2 //
sec⁡(2x+π4)(1−1sec⁡(4x−π2))sec⁡(2x−π4)sec⁡(4x−π2)\frac{\sec{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \frac{1}{\sec{\left(4 x - \frac{\pi}{2} \right)}}\right) \sec{\left(2 x - \frac{\pi}{4} \right)} \sec{\left(4 x - \frac{\pi}{2} \right)}} 
                   2/    pi\                      
             16*tan |x + --|*tan(2*x)             
                    \    8 /                      
--------------------------------------------------
                  2                               
/       2/    pi\\  /       2     \               
|1 + tan |x + --|| *\1 - tan (2*x)/*(1 - sin(4*x))
\        \    8 //
16tan⁡(2x)tan⁡2(x+π8)(1−sin⁡(4x))(1−tan⁡2(2x))(tan⁡2(x+π8)+1)2\frac{16 \tan{\left(2 x \right)} \tan^{2}{\left(x + \frac{\pi}{8} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \left(1 - \tan^{2}{\left(2 x \right)}\right) \left(\tan^{2}{\left(x + \frac{\pi}{8} \right)} + 1\right)^{2}} 
               /       pi\           
            csc|-2*x + --|           
               \       4 /           
-------------------------------------
/       1    \             /      pi\
|1 - --------|*csc(4*x)*csc|2*x + --|
\    csc(4*x)/             \      4 /
csc⁡(−2x+π4)(1−1csc⁡(4x))csc⁡(4x)csc⁡(2x+π4)\frac{\csc{\left(- 2 x + \frac{\pi}{4} \right)}}{\left(1 - \frac{1}{\csc{\left(4 x \right)}}\right) \csc{\left(4 x \right)} \csc{\left(2 x + \frac{\pi}{4} \right)}} 
     2         2         2/      pi\
8*cos (2*x)*sin (2*x)*sin |2*x + --|
                          \      4 /
------------------------------------
  (1 - sin(4*x))*cos(4*x)*sin(4*x)
8sin⁡2(2x)sin⁡2(2x+π4)cos⁡2(2x)(1−sin⁡(4x))sin⁡(4x)cos⁡(4x)\frac{8 \sin^{2}{\left(2 x \right)} \sin^{2}{\left(2 x + \frac{\pi}{4} \right)} \cos^{2}{\left(2 x \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \sin{\left(4 x \right)} \cos{\left(4 x \right)}} 
              /      pi\
2*sin(4*x)*tan|2*x + --|
              \      4 /
------------------------
     2 - 2*sin(4*x)
2sin⁡(4x)tan⁡(2x+π4)2−2sin⁡(4x)\frac{2 \sin{\left(4 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{2 - 2 \sin{\left(4 x \right)}} 
            /      pi\
sin(4*x)*tan|2*x + --|
            \      4 /
----------------------
     1 - sin(4*x)
sin⁡(4x)tan⁡(2x+π4)1−sin⁡(4x)\frac{\sin{\left(4 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{1 - \sin{\left(4 x \right)}} 
     2/      pi\    /      pi\
2*cos |2*x - --|*cos|4*x - --|
      \      4 /    \      2 /
------------------------------
 /       /      pi\\          
 |1 - cos|4*x - --||*cos(4*x) 
 \       \      2 //
2cos⁡2(2x−π4)cos⁡(4x−π2)(1−cos⁡(4x−π2))cos⁡(4x)\frac{2 \cos^{2}{\left(2 x - \frac{\pi}{4} \right)} \cos{\left(4 x - \frac{\pi}{2} \right)}}{\left(1 - \cos{\left(4 x - \frac{\pi}{2} \right)}\right) \cos{\left(4 x \right)}} 
     /      3*pi\    /      pi\  
 -cos|2*x + ----|*cos|4*x - --|  
     \       4  /    \      2 /  
---------------------------------
/       /      pi\\    /      pi\
|1 - cos|4*x - --||*cos|2*x + --|
\       \      2 //    \      4 /
−cos⁡(2x+3π4)cos⁡(4x−π2)(1−cos⁡(4x−π2))cos⁡(2x+π4)- \frac{\cos{\left(2 x + \frac{3 \pi}{4} \right)} \cos{\left(4 x - \frac{\pi}{2} \right)}}{\left(1 - \cos{\left(4 x - \frac{\pi}{2} \right)}\right) \cos{\left(2 x + \frac{\pi}{4} \right)}} 
     2/      pi\         
2*sin |2*x + --|*sin(4*x)
      \      4 /         
-------------------------
 (1 - sin(4*x))*cos(4*x)
2sin⁡(4x)sin⁡2(2x+π4)(1−sin⁡(4x))cos⁡(4x)\frac{2 \sin{\left(4 x \right)} \sin^{2}{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \cos{\left(4 x \right)}} 
               2                               
  /       2   \     4                /      pi\
2*\1 - tan (x)/ *cos (x)*tan(2*x)*tan|2*x + --|
                                     \      4 /
-----------------------------------------------
                  1 - sin(4*x)
2(1−tan⁡2(x))2cos⁡4(x)tan⁡(2x)tan⁡(2x+π4)1−sin⁡(4x)\frac{2 \left(1 - \tan^{2}{\left(x \right)}\right)^{2} \cos^{4}{\left(x \right)} \tan{\left(2 x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{1 - \sin{\left(4 x \right)}} 
                       /       pi\                 
                  2*csc|-2*x + --|                 
                       \       4 /                 
---------------------------------------------------
/       1    \             /pi      \    /      pi\
|1 - --------|*csc(2*x)*csc|-- - 2*x|*csc|2*x + --|
\    csc(4*x)/             \2       /    \      4 /
2csc⁡(−2x+π4)(1−1csc⁡(4x))csc⁡(2x)csc⁡(−2x+π2)csc⁡(2x+π4)\frac{2 \csc{\left(- 2 x + \frac{\pi}{4} \right)}}{\left(1 - \frac{1}{\csc{\left(4 x \right)}}\right) \csc{\left(2 x \right)} \csc{\left(- 2 x + \frac{\pi}{2} \right)} \csc{\left(2 x + \frac{\pi}{4} \right)}} 
               2       /      pi\          
          8*tan (x)*tan|2*x + --|          
                       \      4 /          
-------------------------------------------
             2                             
/       2   \  /      2*tan(2*x) \         
\1 + tan (x)/ *|1 - -------------|*tan(2*x)
               |           2     |         
               \    1 + tan (2*x)/
8tan⁡2(x)tan⁡(2x+π4)(1−2tan⁡(2x)tan⁡2(2x)+1)(tan⁡2(x)+1)2tan⁡(2x)\frac{8 \tan^{2}{\left(x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)}}{\left(1 - \frac{2 \tan{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(2 x \right)}} 
     2       4                /      pi\
8*cot (x)*sin (x)*cot(2*x)*tan|2*x + --|
                              \      4 /
----------------------------------------
              1 - sin(4*x)
8sin⁡4(x)tan⁡(2x+π4)cot⁡2(x)cot⁡(2x)1−sin⁡(4x)\frac{8 \sin^{4}{\left(x \right)} \tan{\left(2 x + \frac{\pi}{4} \right)} \cot^{2}{\left(x \right)} \cot{\left(2 x \right)}}{1 - \sin{\left(4 x \right)}} 
     2*sec(4*x)*sin(4*x)     
-----------------------------
                  2/      pi\
(1 - sin(4*x))*sec |2*x - --|
                   \      4 /
2sin⁡(4x)sec⁡(4x)(1−sin⁡(4x))sec⁡2(2x−π4)\frac{2 \sin{\left(4 x \right)} \sec{\left(4 x \right)}}{\left(1 - \sin{\left(4 x \right)}\right) \sec^{2}{\left(2 x - \frac{\pi}{4} \right)}} 
2*sec(4*x)*sin(4*x)/((1 - sin(4*x))*sec(2*x - pi/4)^2)
    © Sr Examen – Калькулятор