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(z-a)/(5*z-2*a)-(z-4*a)/(z)
z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z)
(x*(x-6)^2)^(1/3)*((x-6)^2/3+x*(-12+2*x)/3)/(x*(x-6)^2)
(((z^2)+(6*z+4))/((z^3)+8))/(1/-1)
Factorizar el polinomio:
z^3+3*z^2
z^2-4*z+16*z^2/16
z^3+z-10
z^3+11*z^2+36*z+26
Descomponer al cuadrado:
x^2*(-2)+5*x-2
-y^4+y^2+5
y^4+y^2-8
-y^4+y^2+9
Expresiones idénticas
sinx/(uno . cinco *sin(2x-2arcsin(sinx/ uno . cinco)))
seno de x dividir por (1.5 multiplicar por seno de (2x menos 2arc seno de ( seno de x dividir por 1.5)))
seno de x dividir por (uno . cinco multiplicar por seno de (2x menos 2arc seno de ( seno de x dividir por uno . cinco)))
sinx/(1.5sin(2x-2arcsin(sinx/1.5)))
sinx/1.5sin2x-2arcsinsinx/1.5
sinx dividir por (1.5*sin(2x-2arcsin(sinx dividir por 1.5)))
Expresiones semejantes
sinx/(1.5*sin(2x+2arcsin(sinx/1.5)))
Expresiones con funciones
sinx
sinx/(4-cos^2x)
sinx/(n*sin(2x-2arcsin(sinx/n)))
sinx/(tan((pi/4)-(x/2))*(1+sinx))
sinx/(((1+tgx/2)/(1-tgx/2))*(1+sinx))
sinx/(((1+tg(x/2))/(1-tg(x/2)))*(1+sinx))
Seno sin
sin(2*a)/((2*tan(a)))
sin(2*x)/((2*cos(2*x)))
sin(a)/((sin(a)-1)*(cos(a)-((sin(a)*cos(a))/(sin(a)-1))))
sin(2*x)/((13*sin(x)))
sin(2*b)/((2*cos(b)))
sinx
sinx/(4-cos^2x)
sinx/(n*sin(2x-2arcsin(sinx/n)))
sinx/(tan((pi/4)-(x/2))*(1+sinx))
sinx/(((1+tgx/2)/(1-tgx/2))*(1+sinx))
sinx/(((1+tg(x/2))/(1-tg(x/2)))*(1+sinx))

Simplificación de expresiones/ Descomposición en fracciones simples/ sinx/(1.5*sin(2x-2arcsin(sinx/1.5)))

¿Cómo vas a descomponer esta sinx/(1.5*sin(2x-2arcsin(sinx/1.5))) expresión en fracciones?

Solución

Ha introducido [src]

            sin(x)           
-----------------------------
/     /            /sin(x)\\\
|3*sin|2*x - 2*asin|------|||
|     \            \ 3/2  //|
|---------------------------|
\             2             /

\frac{\sin{\left(x \right)}}{\frac{3}{2} \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{\frac{3}{2}} \right)} \right)}}

sin(x)/((3*sin(2*x - 2*asin(sin(x)/(3/2)))/2))

Simplificación general [src]

            2*sin(x)           
-------------------------------
     /        /2*sin(x)\      \
3*sin|- 2*asin|--------| + 2*x|
     \        \   3    /      /

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

2*sin(x)/(3*sin(-2*asin(2*sin(x)/3) + 2*x))

Respuesta numérica [src]

0.666666666666667*sin(x)/sin(2*x - 2*asin(sin(x)/(3/2)))

0.666666666666667*sin(x)/sin(2*x - 2*asin(sin(x)/(3/2)))

Unión de expresiones racionales [src]

           2*sin(x)          
-----------------------------
     /  /        /2*sin(x)\\\
3*sin|2*|x - asin|--------|||
     \  \        \   3    ///

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 \left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}\right) \right)}}

2*sin(x)/(3*sin(2*(x - asin(2*sin(x)/3))))

Combinatoria [src]

            2*sin(x)           
-------------------------------
     /        /2*sin(x)\      \
3*sin|- 2*asin|--------| + 2*x|
     \        \   3    /      /

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

2*sin(x)/(3*sin(-2*asin(2*sin(x)/3) + 2*x))

Denominador racional [src]

            2*sin(x)           
-------------------------------
     /        /2*sin(x)\      \
3*sin|- 2*asin|--------| + 2*x|
     \        \   3    /      /

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

2*sin(x)/(3*sin(-2*asin(2*sin(x)/3) + 2*x))

Abrimos la expresión [src]

          2*sin(x)         
---------------------------
     /            /sin(x)\\
3*sin|2*x - 2*asin|------||
     \            \ 3/2  //

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{\frac{3}{2}} \right)} \right)}}

                                                    2*sin(x)                                                   
---------------------------------------------------------------------------------------------------------------
  /                                             _______________                 _______________               \
  |                                            /          2                    /          2                   |
  |                                           /      4*sin (x)                /      4*sin (x)     2          |
  |                        3             4*  /   1 - --------- *sin(x)   8*  /   1 - --------- *cos (x)*sin(x)|
  |                  16*sin (x)*cos(x)     \/            9                 \/            9                    |
3*|2*cos(x)*sin(x) - ----------------- + ----------------------------- - -------------------------------------|
  \                          9                         3                                   3                  /

\frac{2 \sin{\left(x \right)}}{3 \left(- \frac{8 \sqrt{1 - \frac{4 \sin^{2}{\left(x \right)}}{9}} \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{3} + \frac{4 \sqrt{1 - \frac{4 \sin^{2}{\left(x \right)}}{9}} \sin{\left(x \right)}}{3} - \frac{16 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{9} + 2 \sin{\left(x \right)} \cos{\left(x \right)}\right)}

2*sin(x)/(3*(2*cos(x)*sin(x) - 16*sin(x)^3*cos(x)/9 + 4*sqrt(1 - 4*sin(x)^2/9)*sin(x)/3 - 8*sqrt(1 - 4*sin(x)^2/9)*cos(x)^2*sin(x)/3))

Compilar la expresión [src]

          2*sin(x)         
---------------------------
     /            /sin(x)\\
3*sin|2*x - 2*asin|------||
     \            \ 3/2  //

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{\frac{3}{2}} \right)} \right)}}

2*sin(x)/(3*sin(2*x - 2*asin(sin(x)/(3/2))))

Potencias [src]

            2*sin(x)           
-------------------------------
     /        /2*sin(x)\      \
3*sin|- 2*asin|--------| + 2*x|
     \        \   3    /      /

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

                                   /   -I*x    I*x\                                 
                                 2*\- e     + e   /                                 
------------------------------------------------------------------------------------
  /     /             /  /   -I*x    I*x\\\      /            /  /   -I*x    I*x\\\\
  |     |             |I*\- e     + e   /||      |            |I*\- e     + e   /|||
  |   I*|-2*x - 2*asin|------------------||    I*|2*x + 2*asin|------------------|||
  |     \             \        3         //      \            \        3         //|
3*\- e                                      + e                                    /

\frac{2 \left(e^{i x} - e^{- i x}\right)}{3 \left(- e^{i \left(- 2 x - 2 \operatorname{asin}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{3} \right)}\right)} + e^{i \left(2 x + 2 \operatorname{asin}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{3} \right)}\right)}\right)}

2*(-exp(-i*x) + exp(i*x))/(3*(-exp(i*(-2*x - 2*asin(i*(-exp(-i*x) + exp(i*x))/3))) + exp(i*(2*x + 2*asin(i*(-exp(-i*x) + exp(i*x))/3)))))

Parte trigonométrica [src]

     /  /        /2*sin(x)\\\       
2*csc|2*|x - asin|--------|||*sin(x)
     \  \        \   3    ///       
------------------------------------
                 3

\frac{2 \sin{\left(x \right)} \csc{\left(2 \left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}\right) \right)}}{3}

     /        /   2    \\    /pi           /   2    \\
2*csc|x - asin|--------||*csc|-- - x + asin|--------||
     \        \3*csc(x)//    \2            \3*csc(x)//
------------------------------------------------------
                      /x\    /pi   x\                 
                 3*csc|-|*csc|-- - -|                 
                      \2/    \2    2/

\frac{2 \csc{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)} \csc{\left(- x + \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} + \frac{\pi}{2} \right)}}{3 \csc{\left(\frac{x}{2} \right)} \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}

  /        /        /     /    pi\\     \\                                                
  |        |        |2*cos|x - --||     ||                                                
  |       2|        |     \    2 /|   pi||           /        /     /    pi\\\            
  |    cos |x - asin|-------------| - --||           |        |2*cos|x - --|||            
  |        \        \      3      /   2 /|    /x\    |        |     \    2 /||    /x   pi\
2*|1 + ----------------------------------|*cos|-|*cos|x - asin|-------------||*cos|- - --|
  |          /        /     /    pi\\\   |    \2/    \        \      3      //    \2   2 /
  |          |        |2*cos|x - --|||   |                                                
  |         2|        |     \    2 /||   |                                                
  |      cos |x - asin|-------------||   |                                                
  \          \        \      3      //   /                                                
------------------------------------------------------------------------------------------
                                /        /     /    pi\\     \                            
                                |        |2*cos|x - --||     |                            
                                |        |     \    2 /|   pi|                            
                           3*cos|x - asin|-------------| - --|                            
                                \        \      3      /   2 /

\frac{2 \left(1 + \frac{\cos^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3} \right)} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3} \right)} \right)}}\right) \cos{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \cos{\left(x - \operatorname{asin}{\left(\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3} \right)} \right)}}{3 \cos{\left(x - \operatorname{asin}{\left(\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3} \right)} - \frac{\pi}{2} \right)}}

  /        /        /         /x\   \\\       
  |        |        |    4*tan|-|   |||       
  |       2|        |         \2/   |||    /x\
2*|1 + tan |x - asin|---------------|||*tan|-|
  |        |        |  /       2/x\\|||    \2/
  |        |        |3*|1 + tan |-|||||       
  \        \        \  \        \2/////       
----------------------------------------------
                   /        /         /x\   \\
                   |        |    4*tan|-|   ||
  /       2/x\\    |        |         \2/   ||
3*|1 + tan |-||*tan|x - asin|---------------||
  \        \2//    |        |  /       2/x\\||
                   |        |3*|1 + tan |-||||
                   \        \  \        \2////

\frac{2 \left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{4 \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(x - \operatorname{asin}{\left(\frac{4 \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}

       2/x\    4/x\    /x\    /        /2*sin(x)\\ 
  2*cot |-|*sin |-|*cot|-|*tan|x - asin|--------|| 
        \4/     \4/    \2/    \        \   3    // 
---------------------------------------------------
      /        /2*sin(x)\\     /        /2*sin(x)\\
      |x - asin|--------||     |x - asin|--------||
     2|        \   3    /|    4|        \   3    /|
3*cot |------------------|*sin |------------------|
      \        2         /     \        2         /

\frac{2 \sin^{4}{\left(\frac{x}{4} \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)} \cot^{2}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{3 \sin^{4}{\left(\frac{x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}}{2} \right)} \cot^{2}{\left(\frac{x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}}{2} \right)}}

              2*sin(x)              
------------------------------------
     /        /2*sin(x)\         pi\
3*cos|- 2*asin|--------| + 2*x - --|
     \        \   3    /         2 /

\frac{2 \sin{\left(x \right)}}{3 \cos{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} - \frac{\pi}{2} \right)}}

     /        /   2    \      \       
2*csc|- 2*asin|--------| + 2*x|*sin(x)
     \        \3*csc(x)/      /       
--------------------------------------
                  3

\frac{2 \sin{\left(x \right)} \csc{\left(2 x - 2 \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)}}{3}

     /        /      2      \         pi\
2*sec|- 2*asin|-------------| + 2*x - --|
     |        |     /    pi\|         2 |
     |        |3*sec|x - --||           |
     \        \     \    2 //           /
-----------------------------------------
                   /    pi\              
              3*sec|x - --|              
                   \    2 /

\frac{2 \sec{\left(2 x - 2 \operatorname{asin}{\left(\frac{2}{3 \sec{\left(x - \frac{\pi}{2} \right)}} \right)} - \frac{\pi}{2} \right)}}{3 \sec{\left(x - \frac{\pi}{2} \right)}}

                                                           /        /         /x\   \\
                2                                          |        |    4*cot|-|   ||
  /        2/x\\  /                   1               \    |        |         \2/   ||
2*|-1 + cot |-|| *|1 + -------------------------------|*cot|x - asin|---------------||
  \         \4//  |        /        /         /x\   \\|    |        |  /       2/x\\||
                  |        |        |    4*cot|-|   |||    |        |3*|1 + cot |-||||
                  |       2|        |         \2/   |||    \        \  \        \2////
                  |    cot |x - asin|---------------|||                               
                  |        |        |  /       2/x\\|||                               
                  |        |        |3*|1 + cot |-|||||                               
                  \        \        \  \        \2/////                               
--------------------------------------------------------------------------------------
                                              2                                       
                                 /       2/x\\     /x\                                
                               3*|1 + cot |-|| *cot|-|                                
                                 \        \4//     \2/

\frac{2 \left(1 + \frac{1}{\cot^{2}{\left(x - \operatorname{asin}{\left(\frac{4 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \cot{\left(x - \operatorname{asin}{\left(\frac{4 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}

     /pi               /      2      \\
2*sec|-- - 2*x + 2*asin|-------------||
     |2                |     /    pi\||
     |                 |3*sec|x - --|||
     \                 \     \    2 ///
---------------------------------------
                  /    pi\             
             3*sec|x - --|             
                  \    2 /

\frac{2 \sec{\left(- 2 x + 2 \operatorname{asin}{\left(\frac{2}{3 \sec{\left(x - \frac{\pi}{2} \right)}} \right)} + \frac{\pi}{2} \right)}}{3 \sec{\left(x - \frac{\pi}{2} \right)}}

            2*sin(x)           
-------------------------------
     /        /2*sin(x)\      \
3*sin|- 2*asin|--------| + 2*x|
     \        \   3    /      /

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

     /x\    /        /2*sin(x)\\    /        /      2      \\    /x\
2*cos|-|*csc|x - asin|--------||*sec|x - asin|-------------||*sin|-|
     \2/    \        \   3    //    |        |     /    pi\||    \2/
                                    |        |3*sec|x - --|||       
                                    \        \     \    2 ///       
--------------------------------------------------------------------
                                 3

\frac{2 \sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)} \csc{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)} \sec{\left(x - \operatorname{asin}{\left(\frac{2}{3 \sec{\left(x - \frac{\pi}{2} \right)}} \right)} \right)}}{3}

                                       2                                       
  /        /        /         /x\   \\\                                        
  |        |        |    4*tan|-|   |||                                        
  |        |        |         \2/   |||                                        
  |        |    asin|---------------|||                                        
  |        |        |  /       2/x\\|||             /        /         /x\   \\
  |        |        |3*|1 + tan |-|||||             |        |    4*tan|-|   ||
  |       2|x       \  \        \2///||     2/x\    |        |         \2/   ||
2*|1 + tan |- - ---------------------|| *tan |-|*tan|x - asin|---------------||
  \        \2             2          //      \4/    |        |  /       2/x\\||
                                                    |        |3*|1 + tan |-||||
                                                    \        \  \        \2////
-------------------------------------------------------------------------------
                                        /        /         /x\   \\            
                                        |        |    4*tan|-|   ||            
                                        |        |         \2/   ||            
                                        |    asin|---------------||            
                                        |        |  /       2/x\\||            
                           2            |        |3*|1 + tan |-||||            
              /       2/x\\     /x\    2|x       \  \        \2///|            
            3*|1 + tan |-|| *tan|-|*tan |- - ---------------------|            
              \        \4//     \2/     \2             2          /

\frac{2 \left(\tan^{2}{\left(\frac{x}{2} - \frac{\operatorname{asin}{\left(\frac{4 \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{x}{4} \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{4 \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan{\left(\frac{x}{2} \right)} \tan^{2}{\left(\frac{x}{2} - \frac{\operatorname{asin}{\left(\frac{4 \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} \right)}}

                      /x\    /x\                 
                 2*cos|-|*sin|-|                 
                      \2/    \2/                 
-------------------------------------------------
     /        /2*sin(x)\\    /        /2*sin(x)\\
3*cos|x - asin|--------||*sin|x - asin|--------||
     \        \   3    //    \        \   3    //

\frac{2 \sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)}}{3 \sin{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)} \cos{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

                       /           4/        /2*sin(x)\\  \                              
                       |      4*sin |x - asin|--------||  |                              
     2/x\    2/pi   x\ |            \        \   3    //  |    /        /2*sin(x)\      \
2*sin |-|*sin |-- + -|*|1 + ------------------------------|*sin|- 2*asin|--------| + 2*x|
      \2/     \2    2/ |       2/        /2*sin(x)\      \|    \        \   3    /      /
                       |    sin |- 2*asin|--------| + 2*x||                              
                       \        \        \   3    /      //                              
-----------------------------------------------------------------------------------------
                                        2/        /2*sin(x)\\                            
                            3*sin(x)*sin |x - asin|--------||                            
                                         \        \   3    //

\frac{2 \left(\frac{4 \sin^{4}{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}{\sin^{2}{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}} + 1\right) \sin^{2}{\left(\frac{x}{2} \right)} \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)} \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}{3 \sin{\left(x \right)} \sin^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

                2                                                                      
  /        2/x\\     4/x\ /       2/        /2*sin(x)\\\    /        /2*sin(x)\\    /x\
2*|-1 + cot |-|| *sin |-|*|1 + tan |x - asin|--------|||*cot|x - asin|--------||*tan|-|
  \         \4//      \4/ \        \        \   3    ///    \        \   3    //    \2/
---------------------------------------------------------------------------------------
                                           3

\frac{2 \left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)} \cot{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}{3}

     2/x\ /       2/        /2*sin(x)\\\    /x\
2*cos |-|*|1 + tan |x - asin|--------|||*tan|-|
      \2/ \        \        \   3    ///    \2/
-----------------------------------------------
                /        /2*sin(x)\\           
           3*tan|x - asin|--------||           
                \        \   3    //

\frac{2 \left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)} + 1\right) \cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}}{3 \tan{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

                   /    pi\              
              2*cos|x - --|              
                   \    2 /              
-----------------------------------------
     /        /     /    pi\\           \
     |        |2*cos|x - --||           |
     |        |     \    2 /|         pi|
3*cos|- 2*asin|-------------| + 2*x - --|
     \        \      3      /         2 /

\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3 \cos{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3} \right)} - \frac{\pi}{2} \right)}}

                                3*sin(2*x)                               
-------------------------------------------------------------------------
                                         2                               
  /               _______________       \                                
  |     2        /          2           |            /        /2*sin(x)\\
2*\2*sin (x) + \/  9 - 4*sin (x) *cos(x)/ *cos(x)*tan|x - asin|--------||
                                                     \        \   3    //

\frac{3 \sin{\left(2 x \right)}}{2 \left(\sqrt{9 - 4 \sin^{2}{\left(x \right)}} \cos{\left(x \right)} + 2 \sin^{2}{\left(x \right)}\right)^{2} \cos{\left(x \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

               2                                              
  /       2/x\\     4/x\ /       2/        /2*sin(x)\\\    /x\
2*|1 - tan |-|| *cos |-|*|1 + tan |x - asin|--------|||*tan|-|
  \        \4//      \4/ \        \        \   3    ///    \2/
--------------------------------------------------------------
                       /        /2*sin(x)\\                   
                  3*tan|x - asin|--------||                   
                       \        \   3    //

\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)} + 1\right) \cos^{4}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)}}{3 \tan{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

                  /          4/        /2*sin(x)\\ \                            
                  |     4*sin |x - asin|--------|| |                            
     2/x\    2/x\ |           \        \   3    // |    /  /        /2*sin(x)\\\
2*cos |-|*sin |-|*|1 + ----------------------------|*sin|2*|x - asin|--------|||
      \2/     \2/ |       2/  /        /2*sin(x)\\\|    \  \        \   3    ///
                  |    sin |2*|x - asin|--------||||                            
                  \        \  \        \   3    ////                            
--------------------------------------------------------------------------------
                                   2/        /2*sin(x)\\                        
                       3*sin(x)*sin |x - asin|--------||                        
                                    \        \   3    //

\frac{2 \left(\frac{4 \sin^{4}{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}{\sin^{2}{\left(2 \left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}\right) \right)}} + 1\right) \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(2 \left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}\right) \right)} \cos^{2}{\left(\frac{x}{2} \right)}}{3 \sin{\left(x \right)} \sin^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

     /        /   2    \      \
2*csc|- 2*asin|--------| + 2*x|
     \        \3*csc(x)/      /
-------------------------------
            3*csc(x)

\frac{2 \csc{\left(2 x - 2 \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)}}{3 \csc{\left(x \right)}}

     2/        /      2      \   pi\    /        /   2    \\
2*sec |x - asin|-------------| - --|*sec|x - asin|--------||
      |        |     /    pi\|   2 |    \        \3*csc(x)//
      |        |3*sec|x - --||     |                        
      \        \     \    2 //     /                        
------------------------------------------------------------
          /x\    /x   pi\    /        /   2    \   pi\      
     3*sec|-|*sec|- - --|*sec|x - asin|--------| - --|      
          \2/    \2   2 /    \        \3*csc(x)/   2 /

\frac{2 \sec{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)} \sec^{2}{\left(x - \operatorname{asin}{\left(\frac{2}{3 \sec{\left(x - \frac{\pi}{2} \right)}} \right)} - \frac{\pi}{2} \right)}}{3 \sec{\left(\frac{x}{2} \right)} \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \sec{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} - \frac{\pi}{2} \right)}}

                /    pi\            
           2*cos|x - --|            
                \    2 /            
------------------------------------
     /        /2*sin(x)\         pi\
3*cos|- 2*asin|--------| + 2*x - --|
     \        \   3    /         2 /

\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3 \cos{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} - \frac{\pi}{2} \right)}}

     2/x\    /x\    /        /2*sin(x)\\
2*sin |-|*cot|-|*tan|x - asin|--------||
      \2/    \2/    \        \   3    //
----------------------------------------
            2/        /2*sin(x)\\       
       3*sin |x - asin|--------||       
             \        \   3    //

\frac{2 \sin^{2}{\left(\frac{x}{2} \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)} \cot{\left(\frac{x}{2} \right)}}{3 \sin^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

     /pi               /      2      \\
2*sec|-- - 2*x + 2*asin|-------------||
     |2                |     /pi    \||
     |                 |3*sec|-- - x|||
     \                 \     \2     ///
---------------------------------------
                  /    pi\             
             3*sec|x - --|             
                  \    2 /

\frac{2 \sec{\left(- 2 x + 2 \operatorname{asin}{\left(\frac{2}{3 \sec{\left(- x + \frac{\pi}{2} \right)}} \right)} + \frac{\pi}{2} \right)}}{3 \sec{\left(x - \frac{\pi}{2} \right)}}

             4/x\    2/x\    /        /2*sin(x)\\         
        2*cos |-|*tan |-|*tan|x - asin|--------||         
              \4/     \4/    \        \   3    //         
----------------------------------------------------------
      /        /2*sin(x)\\            /        /2*sin(x)\\
      |x - asin|--------||            |x - asin|--------||
     4|        \   3    /|    /x\    2|        \   3    /|
3*cos |------------------|*tan|-|*tan |------------------|
      \        2         /    \2/     \        2         /

\frac{2 \cos^{4}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{4} \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}{3 \cos^{4}{\left(\frac{x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}}{2} \right)} \tan{\left(\frac{x}{2} \right)} \tan^{2}{\left(\frac{x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}}{2} \right)}}

                           /x\    /x   pi\                      
                      2*cos|-|*cos|- - --|                      
                           \2/    \2   2 /                      
----------------------------------------------------------------
     /        /     /    pi\\\    /        /     /    pi\\     \
     |        |2*cos|x - --|||    |        |2*cos|x - --||     |
     |        |     \    2 /||    |        |     \    2 /|   pi|
3*cos|x - asin|-------------||*cos|x - asin|-------------| - --|
     \        \      3      //    \        \      3      /   2 /

\frac{2 \cos{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{3 \cos{\left(x - \operatorname{asin}{\left(\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3} \right)} \right)} \cos{\left(x - \operatorname{asin}{\left(\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{3} \right)} - \frac{\pi}{2} \right)}}

                 /        /        /         /x\   \\\       
               2 |        |        |    4*tan|-|   |||       
  /       2/x\\  |       2|        |         \2/   |||    /x\
2*|1 - tan |-|| *|1 + tan |x - asin|---------------|||*tan|-|
  \        \4//  |        |        |  /       2/x\\|||    \2/
                 |        |        |3*|1 + tan |-|||||       
                 \        \        \  \        \2/////       
-------------------------------------------------------------
                           /        /         /x\   \\       
                      2    |        |    4*tan|-|   ||       
         /       2/x\\     |        |         \2/   ||       
       3*|1 + tan |-|| *tan|x - asin|---------------||       
         \        \4//     |        |  /       2/x\\||       
                           |        |3*|1 + tan |-||||       
                           \        \  \        \2////

\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{4 \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan{\left(x - \operatorname{asin}{\left(\frac{4 \tan{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}

  /          2/        /   2    \\  \                             
  |       sec |x - asin|--------||  |                             
  |           \        \3*csc(x)//  |    /        /   2    \   pi\
2*|1 + -----------------------------|*sec|x - asin|--------| - --|
  |       2/        /   2    \   pi\|    \        \3*csc(x)/   2 /
  |    sec |x - asin|--------| - --||                             
  \        \        \3*csc(x)/   2 //                             
------------------------------------------------------------------
                /x\    /        /   2    \\    /x   pi\           
           3*sec|-|*sec|x - asin|--------||*sec|- - --|           
                \2/    \        \3*csc(x)//    \2   2 /

\frac{2 \left(\frac{\sec^{2}{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)}}{\sec^{2}{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} - \frac{\pi}{2} \right)}}{3 \sec{\left(\frac{x}{2} \right)} \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \sec{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)}}

           2*sin(x)          
-----------------------------
     /  /        /2*sin(x)\\\
3*sin|2*|x - asin|--------|||
     \  \        \   3    ///

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 \left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)}\right) \right)}}

     /x\    /        /   2    \\    /        /2*sin(x)\\    /x\
2*cos|-|*csc|x - asin|--------||*sec|x - asin|--------||*sin|-|
     \2/    \        \3*csc(x)//    \        \   3    //    \2/
---------------------------------------------------------------
                               3

\frac{2 \sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)} \csc{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)} \sec{\left(x - \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}{3}

  /       2/pi           /   2    \\\                        
  |    csc |-- - x + asin|--------|||                        
  |        \2            \3*csc(x)//|    /        /   2    \\
2*|1 + -----------------------------|*csc|x - asin|--------||
  |          2/        /   2    \\  |    \        \3*csc(x)//
  |       csc |x - asin|--------||  |                        
  \           \        \3*csc(x)//  /                        
-------------------------------------------------------------
           /x\    /pi   x\    /pi           /   2    \\      
      3*csc|-|*csc|-- - -|*csc|-- - x + asin|--------||      
           \2/    \2    2/    \2            \3*csc(x)//

\frac{2 \left(1 + \frac{\csc^{2}{\left(- x + \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)}}\right) \csc{\left(x - \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} \right)}}{3 \csc{\left(\frac{x}{2} \right)} \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)} \csc{\left(- x + \operatorname{asin}{\left(\frac{2}{3 \csc{\left(x \right)}} \right)} + \frac{\pi}{2} \right)}}

                                                   2                           
              /        /        /         /x\   \\\                            
              |        |        |    4*cot|-|   |||                            
              |        |        |         \2/   |||                            
              |        |    asin|---------------|||                            
              |        |        |  /       2/x\\|||                            
              |        |        |3*|1 + cot |-|||||                            
              |       2|x       \  \        \2///||     2/x\    /x\            
            2*|1 + cot |- - ---------------------|| *cot |-|*cot|-|            
              \        \2             2          //      \4/    \2/            
-------------------------------------------------------------------------------
                                                    /        /         /x\   \\
                                                    |        |    4*cot|-|   ||
                                                    |        |         \2/   ||
                                                    |    asin|---------------||
                    /        /         /x\   \\     |        |  /       2/x\\||
               2    |        |    4*cot|-|   ||     |        |3*|1 + cot |-||||
  /       2/x\\     |        |         \2/   ||    2|x       \  \        \2///|
3*|1 + cot |-|| *cot|x - asin|---------------||*cot |- - ---------------------|
  \        \4//     |        |  /       2/x\\||     \2             2          /
                    |        |3*|1 + cot |-||||                                
                    \        \  \        \2////

\frac{2 \left(\cot^{2}{\left(\frac{x}{2} - \frac{\operatorname{asin}{\left(\frac{4 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{x}{2} - \frac{\operatorname{asin}{\left(\frac{4 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} \right)} \cot{\left(x - \operatorname{asin}{\left(\frac{4 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}

  /        /        /         /x\   \\\       
  |        |        |    4*cot|-|   |||       
  |       2|        |         \2/   |||    /x\
2*|1 + cot |x - asin|---------------|||*cot|-|
  |        |        |  /       2/x\\|||    \2/
  |        |        |3*|1 + cot |-|||||       
  \        \        \  \        \2/////       
----------------------------------------------
                   /        /         /x\   \\
                   |        |    4*cot|-|   ||
  /       2/x\\    |        |         \2/   ||
3*|1 + cot |-||*cot|x - asin|---------------||
  \        \2//    |        |  /       2/x\\||
                   |        |3*|1 + cot |-||||
                   \        \  \        \2////

\frac{2 \left(\cot^{2}{\left(x - \operatorname{asin}{\left(\frac{4 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(x - \operatorname{asin}{\left(\frac{4 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}

2*(1 + cot(x - asin(4*cot(x/2)/(3*(1 + cot(x/2)^2))))^2)*cot(x/2)/(3*(1 + cot(x/2)^2)*cot(x - asin(4*cot(x/2)/(3*(1 + cot(x/2)^2)))))

Denominador común [src]

            2*sin(x)           
-------------------------------
     /        /2*sin(x)\      \
3*sin|- 2*asin|--------| + 2*x|
     \        \   3    /      /

\frac{2 \sin{\left(x \right)}}{3 \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{2 \sin{\left(x \right)}}{3} \right)} \right)}}

2*sin(x)/(3*sin(-2*asin(2*sin(x)/3) + 2*x))

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