Sr Examen
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))
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))