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Simplificación de expresiones/ Descomposición en fracciones simples/ cot(x)^2*((2+2*tan(x)^2)*tan(x)/cot(x)^2-tan(x)^2*(-2-2*cot(x)^2)/cot(x)^3)/(2*tan(x)^2)

¿Cómo vas a descomponer esta cot(x)^2*((2+2*tan(x)^2)*tan(x)/cot(x)^2-tan(x)^2*(-2-2*cot(x)^2)/cot(x)^3)/(2*tan(x)^2) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
        //         2   \             2    /          2   \\
   2    |\2 + 2*tan (x)/*tan(x)   tan (x)*\-2 - 2*cot (x)/|
cot (x)*|---------------------- - ------------------------|
        |          2                         3            |
        \       cot (x)                   cot (x)         /
-----------------------------------------------------------
                              2                            
                         2*tan (x)
((2tan⁡2(x)+2)tan⁡(x)cot⁡2(x)−(−2cot⁡2(x)−2)tan⁡2(x)cot⁡3(x))cot⁡2(x)2tan⁡2(x)\frac{\left(\frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}}{\cot^{2}{\left(x \right)}} - \frac{\left(- 2 \cot^{2}{\left(x \right)} - 2\right) \tan^{2}{\left(x \right)}}{\cot^{3}{\left(x \right)}}\right) \cot^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)}} 
(cot(x)^2*(((2 + 2*tan(x)^2)*tan(x))/cot(x)^2 - tan(x)^2*(-2 - 2*cot(x)^2)/cot(x)^3))/((2*tan(x)^2))
Simplificación general [src] 
   4    
--------
sin(2*x)
4sin⁡(2x)\frac{4}{\sin{\left(2 x \right)}} 
4/sin(2*x)
Respuesta numérica [src] 
0.5*cot(x)^2*((2.0 + 2.0*tan(x)^2)*tan(x)/cot(x)^2 - tan(x)^2*(-2.0 - 2.0*cot(x)^2)/cot(x)^3)/tan(x)^2
0.5*cot(x)^2*((2.0 + 2.0*tan(x)^2)*tan(x)/cot(x)^2 - tan(x)^2*(-2.0 - 2.0*cot(x)^2)/cot(x)^3)/tan(x)^2
Potencias [src] 
        /   2    /         2   \   /         2   \       \
   2    |tan (x)*\2 + 2*cot (x)/   \2 + 2*tan (x)/*tan(x)|
cot (x)*|----------------------- + ----------------------|
        |            3                        2          |
        \       2*cot (x)                2*cot (x)       /
----------------------------------------------------------
                            2                             
                         tan (x)
((2tan⁡2(x)+2)tan⁡(x)2cot⁡2(x)+(2cot⁡2(x)+2)tan⁡2(x)2cot⁡3(x))cot⁡2(x)tan⁡2(x)\frac{\left(\frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}}{2 \cot^{2}{\left(x \right)}} + \frac{\left(2 \cot^{2}{\left(x \right)} + 2\right) \tan^{2}{\left(x \right)}}{2 \cot^{3}{\left(x \right)}}\right) \cot^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)}} 
                         /                                       /                      2\                 \ 
                         |                                       |      /   I*x    -I*x\ |                 | 
                         |                                       |    2*\- e    + e    / | /   I*x    -I*x\| 
                         |                                     I*|2 - -------------------|*\- e    + e    /| 
                         |                2                      |                    2  |                 | 
               2         |/   I*x    -I*x\  /          2   \     |      / I*x    -I*x\   |                 | 
 / I*x    -I*x\     2    |\- e    + e    / *\-2 - 2*cot (x)/     \      \e    + e    /   /                 | 
-\e    + e    / *cot (x)*|---------------------------------- + --------------------------------------------| 
                         |                   2                            / I*x    -I*x\    2              | 
                         |     / I*x    -I*x\     3                       \e    + e    /*cot (x)           | 
                         \     \e    + e    / *cot (x)                                                     / 
-------------------------------------------------------------------------------------------------------------
                                                               2                                             
                                               /   I*x    -I*x\                                              
                                             2*\- e    + e    /
−(i(−2(−eix+e−ix)2(eix+e−ix)2+2)(−eix+e−ix)(eix+e−ix)cot⁡2(x)+(−eix+e−ix)2(−2cot⁡2(x)−2)(eix+e−ix)2cot⁡3(x))(eix+e−ix)2cot⁡2(x)2(−eix+e−ix)2- \frac{\left(\frac{i \left(- \frac{2 \left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + 2\right) \left(- e^{i x} + e^{- i x}\right)}{\left(e^{i x} + e^{- i x}\right) \cot^{2}{\left(x \right)}} + \frac{\left(- e^{i x} + e^{- i x}\right)^{2} \left(- 2 \cot^{2}{\left(x \right)} - 2\right)}{\left(e^{i x} + e^{- i x}\right)^{2} \cot^{3}{\left(x \right)}}\right) \left(e^{i x} + e^{- i x}\right)^{2} \cot^{2}{\left(x \right)}}{2 \left(- e^{i x} + e^{- i x}\right)^{2}} 
-(exp(i*x) + exp(-i*x))^2*cot(x)^2*((-exp(i*x) + exp(-i*x))^2*(-2 - 2*cot(x)^2)/((exp(i*x) + exp(-i*x))^2*cot(x)^3) + i*(2 - 2*(-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)*(-exp(i*x) + exp(-i*x))/((exp(i*x) + exp(-i*x))*cot(x)^2))/(2*(-exp(i*x) + exp(-i*x))^2)
Denominador común [src] 
cot(x) + tan(x)                  
--------------- + cot(x) + tan(x)
 cot(x)*tan(x)
tan⁡(x)+cot⁡(x)tan⁡(x)cot⁡(x)+tan⁡(x)+cot⁡(x)\frac{\tan{\left(x \right)} + \cot{\left(x \right)}}{\tan{\left(x \right)} \cot{\left(x \right)}} + \tan{\left(x \right)} + \cot{\left(x \right)} 
(cot(x) + tan(x))/(cot(x)*tan(x)) + cot(x) + tan(x)
Denominador racional [src] 
   3    /         2   \             2       2    /          2   \
cot (x)*\2 + 2*tan (x)/*tan(x) - cot (x)*tan (x)*\-2 - 2*cot (x)/
-----------------------------------------------------------------
                             3       2                           
                        2*cot (x)*tan (x)
(2tan⁡2(x)+2)tan⁡(x)cot⁡3(x)−(−2cot⁡2(x)−2)tan⁡2(x)cot⁡2(x)2tan⁡2(x)cot⁡3(x)\frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)} \cot^{3}{\left(x \right)} - \left(- 2 \cot^{2}{\left(x \right)} - 2\right) \tan^{2}{\left(x \right)} \cot^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} \cot^{3}{\left(x \right)}} 
(cot(x)^3*(2 + 2*tan(x)^2)*tan(x) - cot(x)^2*tan(x)^2*(-2 - 2*cot(x)^2))/(2*cot(x)^3*tan(x)^2)
Unión de expresiones racionales [src] 
/       2   \          /        2   \       
\1 + tan (x)/*cot(x) - \-1 - cot (x)/*tan(x)
--------------------------------------------
               cot(x)*tan(x)
(tan⁡2(x)+1)cot⁡(x)−(−cot⁡2(x)−1)tan⁡(x)tan⁡(x)cot⁡(x)\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \left(- \cot^{2}{\left(x \right)} - 1\right) \tan{\left(x \right)}}{\tan{\left(x \right)} \cot{\left(x \right)}} 
((1 + tan(x)^2)*cot(x) - (-1 - cot(x)^2)*tan(x))/(cot(x)*tan(x))
Combinatoria [src] 
(1 + cot(x)*tan(x))*(cot(x) + tan(x))
-------------------------------------
            cot(x)*tan(x)
(tan⁡(x)cot⁡(x)+1)(tan⁡(x)+cot⁡(x))tan⁡(x)cot⁡(x)\frac{\left(\tan{\left(x \right)} \cot{\left(x \right)} + 1\right) \left(\tan{\left(x \right)} + \cot{\left(x \right)}\right)}{\tan{\left(x \right)} \cot{\left(x \right)}} 
(1 + cot(x)*tan(x))*(cot(x) + tan(x))/(cot(x)*tan(x))
Parte trigonométrica [src] 
      4      
-------------
   /      pi\
cos|2*x - --|
   \      2 /
4cos⁡(2x−π2)\frac{4}{\cos{\left(2 x - \frac{\pi}{2} \right)}} 
        /        /         2   \           /          2   \\
        |   3    |    2*sin (x)|      5    |     2*cos (x)||
        |sin (x)*|2 + ---------|   sin (x)*|-2 - ---------||
        |        |        2    |           |         2    ||
   4    |        \     cos (x) /           \      sin (x) /|
cos (x)*|----------------------- - ------------------------|
        |           3                         5            |
        \        cos (x)                   cos (x)         /
------------------------------------------------------------
                              4                             
                         2*sin (x)
(−(−2−2cos⁡2(x)sin⁡2(x))sin⁡5(x)cos⁡5(x)+(2sin⁡2(x)cos⁡2(x)+2)sin⁡3(x)cos⁡3(x))cos⁡4(x)2sin⁡4(x)\frac{\left(- \frac{\left(-2 - \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{5}{\left(x \right)}}{\cos^{5}{\left(x \right)}} + \frac{\left(\frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2\right) \sin^{3}{\left(x \right)}}{\cos^{3}{\left(x \right)}}\right) \cos^{4}{\left(x \right)}}{2 \sin^{4}{\left(x \right)}} 
   4    
--------
sin(2*x)
4sin⁡(2x)\frac{4}{\sin{\left(2 x \right)}} 
        /             /         2/pi    \\                /           2     \\
        |             |    2*csc |-- - x||      5/pi    \ |      2*csc (x)  ||
        |   3/pi    \ |          \2     /|   csc |-- - x|*|-2 - ------------||
        |csc |-- - x|*|2 + --------------|       \2     / |        2/pi    \||
        |    \2     / |          2       |                |     csc |-- - x|||
   4    |             \       csc (x)    /                \         \2     //|
csc (x)*|--------------------------------- - --------------------------------|
        |                3                                  5                |
        \             csc (x)                            csc (x)             /
------------------------------------------------------------------------------
                                     4/pi    \                                
                                2*csc |-- - x|                                
                                      \2     /
((2+2csc⁡2(−x+π2)csc⁡2(x))csc⁡3(−x+π2)csc⁡3(x)−(−2csc⁡2(x)csc⁡2(−x+π2)−2)csc⁡5(−x+π2)csc⁡5(x))csc⁡4(x)2csc⁡4(−x+π2)\frac{\left(\frac{\left(2 + \frac{2 \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right) \csc^{3}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{3}{\left(x \right)}} - \frac{\left(- \frac{2 \csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - 2\right) \csc^{5}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{5}{\left(x \right)}}\right) \csc^{4}{\left(x \right)}}{2 \csc^{4}{\left(- x + \frac{\pi}{2} \right)}} 
        /        /         2   \           /          2   \\
        |   3    |    2*sec (x)|      5    |     2*csc (x)||
        |sec (x)*|2 + ---------|   sec (x)*|-2 - ---------||
        |        |        2    |           |         2    ||
   4    |        \     csc (x) /           \      sec (x) /|
csc (x)*|----------------------- - ------------------------|
        |           3                         5            |
        \        csc (x)                   csc (x)         /
------------------------------------------------------------
                              4                             
                         2*sec (x)
((2+2sec⁡2(x)csc⁡2(x))sec⁡3(x)csc⁡3(x)−(−2csc⁡2(x)sec⁡2(x)−2)sec⁡5(x)csc⁡5(x))csc⁡4(x)2sec⁡4(x)\frac{\left(\frac{\left(2 + \frac{2 \sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right) \sec^{3}{\left(x \right)}}{\csc^{3}{\left(x \right)}} - \frac{\left(- \frac{2 \csc^{2}{\left(x \right)}}{\sec^{2}{\left(x \right)}} - 2\right) \sec^{5}{\left(x \right)}}{\csc^{5}{\left(x \right)}}\right) \csc^{4}{\left(x \right)}}{2 \sec^{4}{\left(x \right)}} 
     /      pi\
4*sec|2*x - --|
     \      2 /
4sec⁡(2x−π2)4 \sec{\left(2 x - \frac{\pi}{2} \right)} 
  /       2   \
2*\1 + cot (x)/
---------------
     cot(x)
2(cot⁡2(x)+1)cot⁡(x)\frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} 
  /       2   \
2*\1 + tan (x)/
---------------
     tan(x)
2(tan⁡2(x)+1)tan⁡(x)\frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} 
        /       2                    \
        |2 + -------                 |
        |       2                2   |
   4    |    cot (x)   -2 - 2*cot (x)|
cot (x)*|----------- - --------------|
        |     3              5       |
        \  cot (x)        cot (x)    /
--------------------------------------
                  2
(2+2cot⁡2(x)cot⁡3(x)−−2cot⁡2(x)−2cot⁡5(x))cot⁡4(x)2\frac{\left(\frac{2 + \frac{2}{\cot^{2}{\left(x \right)}}}{\cot^{3}{\left(x \right)}} - \frac{- 2 \cot^{2}{\left(x \right)} - 2}{\cot^{5}{\left(x \right)}}\right) \cot^{4}{\left(x \right)}}{2} 
   3    /         2   \      5    /        2   \
tan (x)*\2 + 2*tan (x)/ - tan (x)*|-2 - -------|
                                  |        2   |
                                  \     tan (x)/
------------------------------------------------
                        4                       
                   2*tan (x)
−(−2−2tan⁡2(x))tan⁡5(x)+(2tan⁡2(x)+2)tan⁡3(x)2tan⁡4(x)\frac{- \left(-2 - \frac{2}{\tan^{2}{\left(x \right)}}\right) \tan^{5}{\left(x \right)} + \left(2 \tan^{2}{\left(x \right)} + 2\right) \tan^{3}{\left(x \right)}}{2 \tan^{4}{\left(x \right)}} 
        /             /         2/    pi\\                /           2     \\
        |             |    2*cos |x - --||      5/    pi\ |      2*cos (x)  ||
        |   3/    pi\ |          \    2 /|   cos |x - --|*|-2 - ------------||
        |cos |x - --|*|2 + --------------|       \    2 / |        2/    pi\||
        |    \    2 / |          2       |                |     cos |x - --|||
   4    |             \       cos (x)    /                \         \    2 //|
cos (x)*|--------------------------------- - --------------------------------|
        |                3                                  5                |
        \             cos (x)                            cos (x)             /
------------------------------------------------------------------------------
                                     4/    pi\                                
                                2*cos |x - --|                                
                                      \    2 /
((2+2cos⁡2(x−π2)cos⁡2(x))cos⁡3(x−π2)cos⁡3(x)−(−2cos⁡2(x)cos⁡2(x−π2)−2)cos⁡5(x−π2)cos⁡5(x))cos⁡4(x)2cos⁡4(x−π2)\frac{\left(\frac{\left(2 + \frac{2 \cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right) \cos^{3}{\left(x - \frac{\pi}{2} \right)}}{\cos^{3}{\left(x \right)}} - \frac{\left(- \frac{2 \cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} - 2\right) \cos^{5}{\left(x - \frac{\pi}{2} \right)}}{\cos^{5}{\left(x \right)}}\right) \cos^{4}{\left(x \right)}}{2 \cos^{4}{\left(x - \frac{\pi}{2} \right)}} 
4*csc(2*x)
4csc⁡(2x)4 \csc{\left(2 x \right)} 
          /              /        2     \             /         4   \\
          |        10    |     sin (2*x)|        6    |    8*sin (x)||
          |  32*sin  (x)*|-2 - ---------|   8*sin (x)*|2 + ---------||
          |              |          4   |             |       2     ||
   4      |              \     2*sin (x)/             \    sin (2*x)/|
sin (2*x)*|- ---------------------------- + -------------------------|
          |              5                             3             |
          \           sin (2*x)                     sin (2*x)        /
----------------------------------------------------------------------
                                    8                                 
                              32*sin (x)
(−32(−2−sin⁡2(2x)2sin⁡4(x))sin⁡10(x)sin⁡5(2x)+8(8sin⁡4(x)sin⁡2(2x)+2)sin⁡6(x)sin⁡3(2x))sin⁡4(2x)32sin⁡8(x)\frac{\left(- \frac{32 \left(-2 - \frac{\sin^{2}{\left(2 x \right)}}{2 \sin^{4}{\left(x \right)}}\right) \sin^{10}{\left(x \right)}}{\sin^{5}{\left(2 x \right)}} + \frac{8 \left(\frac{8 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 2\right) \sin^{6}{\left(x \right)}}{\sin^{3}{\left(2 x \right)}}\right) \sin^{4}{\left(2 x \right)}}{32 \sin^{8}{\left(x \right)}} 
             /        /          2     \           /          2/    pi\\\
             |   3    |     2*sec (x)  |           |     2*sec |x - --|||
             |sec (x)*|2 + ------------|      5    |           \    2 /||
             |        |       2/    pi\|   sec (x)*|-2 - --------------||
             |        |    sec |x - --||           |           2       ||
   4/    pi\ |        \        \    2 //           \        sec (x)    /|
sec |x - --|*|-------------------------- - -----------------------------|
    \    2 / |          3/    pi\                      5/    pi\        |
             |       sec |x - --|                   sec |x - --|        |
             \           \    2 /                       \    2 /        /
-------------------------------------------------------------------------
                                     4                                   
                                2*sec (x)
(−(−2−2sec⁡2(x−π2)sec⁡2(x))sec⁡5(x)sec⁡5(x−π2)+(2sec⁡2(x)sec⁡2(x−π2)+2)sec⁡3(x)sec⁡3(x−π2))sec⁡4(x−π2)2sec⁡4(x)\frac{\left(- \frac{\left(-2 - \frac{2 \sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}}\right) \sec^{5}{\left(x \right)}}{\sec^{5}{\left(x - \frac{\pi}{2} \right)}} + \frac{\left(\frac{2 \sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 2\right) \sec^{3}{\left(x \right)}}{\sec^{3}{\left(x - \frac{\pi}{2} \right)}}\right) \sec^{4}{\left(x - \frac{\pi}{2} \right)}}{2 \sec^{4}{\left(x \right)}} 
sec(x - pi/2)^4*(sec(x)^3*(2 + 2*sec(x)^2/sec(x - pi/2)^2)/sec(x - pi/2)^3 - sec(x)^5*(-2 - 2*sec(x - pi/2)^2/sec(x)^2)/sec(x - pi/2)^5)/(2*sec(x)^4)
Abrimos la expresión [src] 
  1        1                     
------ + ------ + cot(x) + tan(x)
cot(x)   tan(x)
tan⁡(x)+cot⁡(x)+1cot⁡(x)+1tan⁡(x)\tan{\left(x \right)} + \cot{\left(x \right)} + \frac{1}{\cot{\left(x \right)}} + \frac{1}{\tan{\left(x \right)}} 
1/cot(x) + 1/tan(x) + cot(x) + tan(x)
    © Sr Examen – Калькулятор