Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sinx/(n*sin(2x-2arcsin(sinx/n)))
¿Cómo vas a descomponer esta sinx/(n*sin(2x-2arcsin(sinx/n))) expresión en fracciones?
Solución
Ha introducido
[src]
sin(x)
---------------------------
/ /sin(x)\\
n*sin|2*x - 2*asin|------||
\ \ n //
$$\frac{\sin{\left(x \right)}}{n \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}$$
sin(x)/((n*sin(2*x - 2*asin(sin(x)/n))))
Respuesta numérica
[src]
sin(x)/(n*sin(2*x - 2*asin(sin(x)/n)))
sin(x)/(n*sin(2*x - 2*asin(sin(x)/n)))
Unión de expresiones racionales
[src]
sin(x)
---------------------------
/ / /sin(x)\\\
n*sin|2*|x - asin|------|||
\ \ \ n ///
$$\frac{\sin{\left(x \right)}}{n \sin{\left(2 \left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}\right) \right)}}$$
sin(x)/(n*sin(2*(x - asin(sin(x)/n))))
Potencias
[src]
-I*x I*x
- 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|------------------|||
| \ \ 2*n // \ \ 2*n //|
n*\- e + e /
$$\frac{e^{i x} - e^{- i x}}{n \left(- e^{i \left(- 2 x - 2 \operatorname{asin}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2 n} \right)}\right)} + e^{i \left(2 x + 2 \operatorname{asin}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2 n} \right)}\right)}\right)}$$
(-exp(-i*x) + exp(i*x))/(n*(-exp(i*(-2*x - 2*asin(i*(-exp(-i*x) + exp(i*x))/(2*n)))) + exp(i*(2*x + 2*asin(i*(-exp(-i*x) + exp(i*x))/(2*n))))))
Parte trigonométrica
[src]
/x\ /x pi\
cos|-|*cos|- - --|
\2/ \2 2 /
------------------------------------------------------------
/ / / pi\\\ / / / pi\\ \
| |cos|x - --||| | |cos|x - --|| |
| | \ 2 /|| | | \ 2 /| pi|
n*cos|x - asin|-----------||*cos|x - asin|-----------| - --|
\ \ n // \ \ n / 2 /
$$\frac{\cos{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{n \cos{\left(x - \operatorname{asin}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n} \right)} \right)} \cos{\left(x - \operatorname{asin}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n} \right)} - \frac{\pi}{2} \right)}}$$
/ 2/ / 1 \\ \
| sec |x - asin|--------|| |
| \ \n*csc(x)// | / / 1 \ pi\
|1 + -----------------------------|*sec|x - asin|--------| - --|
| 2/ / 1 \ pi\| \ \n*csc(x)/ 2 /
| sec |x - asin|--------| - --||
\ \ \n*csc(x)/ 2 //
----------------------------------------------------------------
/x\ / / 1 \\ /x pi\
n*sec|-|*sec|x - asin|--------||*sec|- - --|
\2/ \ \n*csc(x)// \2 2 /
$$\frac{\left(\frac{\sec^{2}{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)}}{\sec^{2}{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} - \frac{\pi}{2} \right)}}{n \sec{\left(\frac{x}{2} \right)} \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \sec{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)}}$$
/x\ /x\
cos|-|*sin|-|
\2/ \2/
---------------------------------------------
/ /sin(x)\\ / /sin(x)\\
n*cos|x - asin|------||*sin|x - asin|------||
\ \ n // \ \ n //
$$\frac{\sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)}}{n \sin{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)} \cos{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}$$
sin(x)
----------------------------------
/ /sin(x)\ pi\
n*cos|- 2*asin|------| + 2*x - --|
\ \ n / 2 /
$$\frac{\sin{\left(x \right)}}{n \cos{\left(2 x - 2 \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} - \frac{\pi}{2} \right)}}$$
/ / / /x\ \\\
2 | | | 2*tan|-| |||
/ 2/x\\ | 2| | \2/ ||| /x\
|1 - tan |-|| *|1 + tan |x - asin|---------------|||*tan|-|
\ \4// | | | / 2/x\\||| \2/
| | |n*|1 + tan |-|||||
\ \ \ \ \2/////
-----------------------------------------------------------
/ / /x\ \\
2 | | 2*tan|-| ||
/ 2/x\\ | | \2/ ||
n*|1 + tan |-|| *tan|x - asin|---------------||
\ \4// | | / 2/x\\||
| |n*|1 + tan |-||||
\ \ \ \2////
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan{\left(x - \operatorname{asin}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}$$
2
/ / / /x\ \\\
| | | 2*tan|-| |||
| | | \2/ |||
| | asin|---------------|||
| | | / 2/x\\||| / / /x\ \\
| | |n*|1 + tan |-||||| | | 2*tan|-| ||
| 2|x \ \ \2///|| 2/x\ | | \2/ ||
|1 + tan |- - ---------------------|| *tan |-|*tan|x - asin|---------------||
\ \2 2 // \4/ | | / 2/x\\||
| |n*|1 + tan |-||||
\ \ \ \2////
-----------------------------------------------------------------------------
/ / /x\ \\
| | 2*tan|-| ||
| | \2/ ||
| asin|---------------||
| | / 2/x\\||
2 | |n*|1 + tan |-||||
/ 2/x\\ /x\ 2|x \ \ \2///|
n*|1 + tan |-|| *tan|-|*tan |- - ---------------------|
\ \4// \2/ \2 2 /
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} - \frac{\operatorname{asin}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{x}{4} \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}{n \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \tan{\left(\frac{x}{2} \right)} \tan^{2}{\left(\frac{x}{2} - \frac{\operatorname{asin}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} \right)}}$$
/ / 1 \ \
csc|- 2*asin|--------| + 2*x|
\ \n*csc(x)/ /
-----------------------------
n*csc(x)
$$\frac{\csc{\left(2 x - 2 \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)}}{n \csc{\left(x \right)}}$$
sin(x)
---------------------------
/ / /sin(x)\\\
n*sin|2*|x - asin|------|||
\ \ \ n ///
$$\frac{\sin{\left(x \right)}}{n \sin{\left(2 \left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}\right) \right)}}$$
/pi / 1 \\
sec|-- - 2*x + 2*asin|-------------||
|2 | /pi \||
| |n*sec|-- - x|||
\ \ \2 ///
-------------------------------------
/ pi\
n*sec|x - --|
\ 2 /
$$\frac{\sec{\left(- 2 x + 2 \operatorname{asin}{\left(\frac{1}{n \sec{\left(- x + \frac{\pi}{2} \right)}} \right)} + \frac{\pi}{2} \right)}}{n \sec{\left(x - \frac{\pi}{2} \right)}}$$
/ / 1 \ pi\
sec|- 2*asin|-------------| + 2*x - --|
| | / pi\| 2 |
| |n*sec|x - --|| |
\ \ \ 2 // /
---------------------------------------
/ pi\
n*sec|x - --|
\ 2 /
$$\frac{\sec{\left(2 x - 2 \operatorname{asin}{\left(\frac{1}{n \sec{\left(x - \frac{\pi}{2} \right)}} \right)} - \frac{\pi}{2} \right)}}{n \sec{\left(x - \frac{\pi}{2} \right)}}$$
/x\ / / 1 \\ / /sin(x)\\ /x\
cos|-|*csc|x - asin|--------||*sec|x - asin|------||*sin|-|
\2/ \ \n*csc(x)// \ \ n // \2/
-----------------------------------------------------------
n
$$\frac{\sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)} \csc{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)} \sec{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}{n}$$
/ 2/pi / 1 \\\
| csc |-- - x + asin|--------|||
| \2 \n*csc(x)//| / / 1 \\
|1 + -----------------------------|*csc|x - asin|--------||
| 2/ / 1 \\ | \ \n*csc(x)//
| csc |x - asin|--------|| |
\ \ \n*csc(x)// /
-----------------------------------------------------------
/x\ /pi x\ /pi / 1 \\
n*csc|-|*csc|-- - -|*csc|-- - x + asin|--------||
\2/ \2 2/ \2 \n*csc(x)//
$$\frac{\left(1 + \frac{\csc^{2}{\left(- x + \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)}}\right) \csc{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)}}{n \csc{\left(\frac{x}{2} \right)} \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)} \csc{\left(- x + \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} + \frac{\pi}{2} \right)}}$$
/ / /x\ \\
2 | | 2*cot|-| ||
/ 2/x\\ / 1 \ | | \2/ ||
|-1 + cot |-|| *|1 + -------------------------------|*cot|x - asin|---------------||
\ \4// | / / /x\ \\| | | / 2/x\\||
| | | 2*cot|-| ||| | |n*|1 + cot |-||||
| 2| | \2/ ||| \ \ \ \2////
| cot |x - asin|---------------|||
| | | / 2/x\\|||
| | |n*|1 + cot |-|||||
\ \ \ \ \2/////
------------------------------------------------------------------------------------
2
/ 2/x\\ /x\
n*|1 + cot |-|| *cot|-|
\ \4// \2/
$$\frac{\left(1 + \frac{1}{\cot^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \cot{\left(x - \operatorname{asin}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}{n \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}$$
2/x\ /x\ / /sin(x)\\
sin |-|*cot|-|*tan|x - asin|------||
\2/ \2/ \ \ n //
------------------------------------
2/ /sin(x)\\
n*sin |x - asin|------||
\ \ n //
$$\frac{\sin^{2}{\left(\frac{x}{2} \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)} \cot{\left(\frac{x}{2} \right)}}{n \sin^{2}{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}$$
/ pi\
cos|x - --|
\ 2 /
----------------------------------
/ /sin(x)\ pi\
n*cos|- 2*asin|------| + 2*x - --|
\ \ n / 2 /
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n \cos{\left(2 x - 2 \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} - \frac{\pi}{2} \right)}}$$
2
/ / / /x\ \\\
| | | 2*cot|-| |||
| | | \2/ |||
| | asin|---------------|||
| | | / 2/x\\|||
| | |n*|1 + cot |-|||||
| 2|x \ \ \2///|| 2/x\ /x\
|1 + cot |- - ---------------------|| *cot |-|*cot|-|
\ \2 2 // \4/ \2/
-------------------------------------------------------------------------------
/ / /x\ \\
| | 2*cot|-| ||
| | \2/ ||
| asin|---------------||
/ / /x\ \\ | | / 2/x\\||
2 | | 2*cot|-| || | |n*|1 + cot |-||||
/ 2/x\\ | | \2/ || 2|x \ \ \2///|
n*|1 + cot |-|| *cot|x - asin|---------------||*cot |- - ---------------------|
\ \4// | | / 2/x\\|| \2 2 /
| |n*|1 + cot |-||||
\ \ \ \2////
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} - \frac{\operatorname{asin}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{x}{2} - \frac{\operatorname{asin}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)}}{2} \right)} \cot{\left(x - \operatorname{asin}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}$$
4/x\ 2/x\ / /sin(x)\\
cos |-|*tan |-|*tan|x - asin|------||
\4/ \4/ \ \ n //
------------------------------------------------------
/ /sin(x)\\ / /sin(x)\\
|x - asin|------|| |x - asin|------||
4| \ n /| /x\ 2| \ n /|
n*cos |----------------|*tan|-|*tan |----------------|
\ 2 / \2/ \ 2 /
$$\frac{\cos^{4}{\left(\frac{x}{4} \right)} \tan^{2}{\left(\frac{x}{4} \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}{n \cos^{4}{\left(\frac{x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}}{2} \right)} \tan{\left(\frac{x}{2} \right)} \tan^{2}{\left(\frac{x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}}{2} \right)}}$$
2/ / 1 \ pi\ / / 1 \\
sec |x - asin|-------------| - --|*sec|x - asin|--------||
| | / pi\| 2 | \ \n*csc(x)//
| |n*sec|x - --|| |
\ \ \ 2 // /
----------------------------------------------------------
/x\ /x pi\ / / 1 \ pi\
n*sec|-|*sec|- - --|*sec|x - asin|--------| - --|
\2/ \2 2 / \ \n*csc(x)/ 2 /
$$\frac{\sec{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)} \sec^{2}{\left(x - \operatorname{asin}{\left(\frac{1}{n \sec{\left(x - \frac{\pi}{2} \right)}} \right)} - \frac{\pi}{2} \right)}}{n \sec{\left(\frac{x}{2} \right)} \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \sec{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} - \frac{\pi}{2} \right)}}$$
2/x\ / 2/ /sin(x)\\\ /x\
cos |-|*|1 + tan |x - asin|------|||*tan|-|
\2/ \ \ \ n /// \2/
-------------------------------------------
/ /sin(x)\\
n*tan|x - asin|------||
\ \ n //
$$\frac{\left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)} + 1\right) \cos^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} \right)}}{n \tan{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}$$
/pi / 1 \\
sec|-- - 2*x + 2*asin|-------------||
|2 | / pi\||
| |n*sec|x - --|||
\ \ \ 2 ///
-------------------------------------
/ pi\
n*sec|x - --|
\ 2 /
$$\frac{\sec{\left(- 2 x + 2 \operatorname{asin}{\left(\frac{1}{n \sec{\left(x - \frac{\pi}{2} \right)}} \right)} + \frac{\pi}{2} \right)}}{n \sec{\left(x - \frac{\pi}{2} \right)}}$$
n*sin(2*x)
------------------------------------------------------------------------
2
/ _____________ \
| / 2 |
| 2 / sin (x) | / /sin(x)\\
4*|sin (x) + n* / 1 - ------- *cos(x)| *cos(x)*tan|x - asin|------||
| / 2 | \ \ n //
\ \/ n /
$$\frac{n \sin{\left(2 x \right)}}{4 \left(n \sqrt{1 - \frac{\sin^{2}{\left(x \right)}}{n^{2}}} \cos{\left(x \right)} + \sin^{2}{\left(x \right)}\right)^{2} \cos{\left(x \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}$$
/ 4/ /sin(x)\\ \
| 4*sin |x - asin|------|| |
2/x\ 2/pi x\ | \ \ n // | / /sin(x)\ \
sin |-|*sin |-- + -|*|1 + ----------------------------|*sin|- 2*asin|------| + 2*x|
\2/ \2 2/ | 2/ /sin(x)\ \| \ \ n / /
| sin |- 2*asin|------| + 2*x||
\ \ \ n / //
-----------------------------------------------------------------------------------
2/ /sin(x)\\
n*sin(x)*sin |x - asin|------||
\ \ n //
$$\frac{\left(\frac{4 \sin^{4}{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}{\sin^{2}{\left(2 x - 2 \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}} + 1\right) \sin^{2}{\left(\frac{x}{2} \right)} \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)} \sin{\left(2 x - 2 \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}{n \sin{\left(x \right)} \sin^{2}{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}$$
/ 4/ /sin(x)\\ \
| 4*sin |x - asin|------|| |
2/x\ 2/x\ | \ \ n // | / / /sin(x)\\\
cos |-|*sin |-|*|1 + --------------------------|*sin|2*|x - asin|------|||
\2/ \2/ | 2/ / /sin(x)\\\| \ \ \ n ///
| sin |2*|x - asin|------||||
\ \ \ \ n ////
--------------------------------------------------------------------------
2/ /sin(x)\\
n*sin(x)*sin |x - asin|------||
\ \ n //
$$\frac{\left(\frac{4 \sin^{4}{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}{\sin^{2}{\left(2 \left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}\right) \right)}} + 1\right) \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(2 \left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}\right) \right)} \cos^{2}{\left(\frac{x}{2} \right)}}{n \sin{\left(x \right)} \sin^{2}{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}$$
/x\ / /sin(x)\\ / / 1 \\ /x\
cos|-|*csc|x - asin|------||*sec|x - asin|-------------||*sin|-|
\2/ \ \ n // | | / pi\|| \2/
| |n*sec|x - --|||
\ \ \ 2 ///
----------------------------------------------------------------
n
$$\frac{\sin{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} \right)} \csc{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)} \sec{\left(x - \operatorname{asin}{\left(\frac{1}{n \sec{\left(x - \frac{\pi}{2} \right)}} \right)} \right)}}{n}$$
/ / 1 \ \
csc|- 2*asin|--------| + 2*x|*sin(x)
\ \n*csc(x)/ /
------------------------------------
n
$$\frac{\sin{\left(x \right)} \csc{\left(2 x - 2 \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)}}{n}$$
/ / /sin(x)\\\
csc|2*|x - asin|------|||*sin(x)
\ \ \ n ///
--------------------------------
n
$$\frac{\sin{\left(x \right)} \csc{\left(2 \left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}\right) \right)}}{n}$$
/ / / /x\ \\\
| | | 2*tan|-| |||
| 2| | \2/ ||| /x\
|1 + tan |x - asin|---------------|||*tan|-|
| | | / 2/x\\||| \2/
| | |n*|1 + tan |-|||||
\ \ \ \ \2/////
----------------------------------------------
/ / /x\ \\
| | 2*tan|-| ||
/ 2/x\\ | | \2/ ||
n*|1 + tan |-||*tan|x - asin|---------------||
\ \2// | | / 2/x\\||
| |n*|1 + tan |-||||
\ \ \ \2////
$$\frac{\left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(x - \operatorname{asin}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{n \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}$$
/ / 1 \\ /pi / 1 \\
csc|x - asin|--------||*csc|-- - x + asin|--------||
\ \n*csc(x)// \2 \n*csc(x)//
----------------------------------------------------
/x\ /pi x\
n*csc|-|*csc|-- - -|
\2/ \2 2/
$$\frac{\csc{\left(x - \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} \right)} \csc{\left(- x + \operatorname{asin}{\left(\frac{1}{n \csc{\left(x \right)}} \right)} + \frac{\pi}{2} \right)}}{n \csc{\left(\frac{x}{2} \right)} \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}$$
/ / / /x\ \\\
| | | 2*cot|-| |||
| 2| | \2/ ||| /x\
|1 + cot |x - asin|---------------|||*cot|-|
| | | / 2/x\\||| \2/
| | |n*|1 + cot |-|||||
\ \ \ \ \2/////
----------------------------------------------
/ / /x\ \\
| | 2*cot|-| ||
/ 2/x\\ | | \2/ ||
n*|1 + cot |-||*cot|x - asin|---------------||
\ \2// | | / 2/x\\||
| |n*|1 + cot |-||||
\ \ \ \2////
$$\frac{\left(\cot^{2}{\left(x - \operatorname{asin}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(x - \operatorname{asin}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{n \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} \right)} \right)}}$$
2
/ 2/x\\ 4/x\ / 2/ /sin(x)\\\ /x\
|1 - tan |-|| *cos |-|*|1 + tan |x - asin|------|||*tan|-|
\ \4// \4/ \ \ \ n /// \2/
----------------------------------------------------------
/ /sin(x)\\
n*tan|x - asin|------||
\ \ n //
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)} + 1\right) \cos^{4}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)}}{n \tan{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}$$
/ pi\
cos|x - --|
\ 2 /
---------------------------------------
/ / / pi\\ \
| |cos|x - --|| |
| | \ 2 /| pi|
n*cos|- 2*asin|-----------| + 2*x - --|
\ \ n / 2 /
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n \cos{\left(2 x - 2 \operatorname{asin}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n} \right)} - \frac{\pi}{2} \right)}}$$
2
/ 2/x\\ 4/x\ / 2/ /sin(x)\\\ / /sin(x)\\ /x\
|-1 + cot |-|| *sin |-|*|1 + tan |x - asin|------|||*cot|x - asin|------||*tan|-|
\ \4// \4/ \ \ \ n /// \ \ n // \2/
---------------------------------------------------------------------------------
n
$$\frac{\left(\tan^{2}{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)} \cot{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)}}{n}$$
/ / / / pi\\ \\
| | |cos|x - --|| ||
| 2| | \ 2 /| pi|| / / / pi\\\
| cos |x - asin|-----------| - --|| | |cos|x - --|||
| \ \ n / 2 /| /x\ | | \ 2 /|| /x pi\
|1 + --------------------------------|*cos|-|*cos|x - asin|-----------||*cos|- - --|
| / / / pi\\\ | \2/ \ \ n // \2 2 /
| | |cos|x - --||| |
| 2| | \ 2 /|| |
| cos |x - asin|-----------|| |
\ \ \ n // /
------------------------------------------------------------------------------------
/ / / pi\\ \
| |cos|x - --|| |
| | \ 2 /| pi|
n*cos|x - asin|-----------| - --|
\ \ n / 2 /
$$\frac{\left(1 + \frac{\cos^{2}{\left(x - \operatorname{asin}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n} \right)} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x - \operatorname{asin}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n} \right)} \right)}}\right) \cos{\left(\frac{x}{2} \right)} \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)} \cos{\left(x - \operatorname{asin}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n} \right)} \right)}}{n \cos{\left(x - \operatorname{asin}{\left(\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{n} \right)} - \frac{\pi}{2} \right)}}$$
2/x\ 4/x\ /x\ / /sin(x)\\
cot |-|*sin |-|*cot|-|*tan|x - asin|------||
\4/ \4/ \2/ \ \ n //
-----------------------------------------------
/ /sin(x)\\ / /sin(x)\\
|x - asin|------|| |x - asin|------||
2| \ n /| 4| \ n /|
n*cot |----------------|*sin |----------------|
\ 2 / \ 2 /
$$\frac{\sin^{4}{\left(\frac{x}{4} \right)} \tan{\left(x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)} \right)} \cot^{2}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{n \sin^{4}{\left(\frac{x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}}{2} \right)} \cot^{2}{\left(\frac{x - \operatorname{asin}{\left(\frac{\sin{\left(x \right)}}{n} \right)}}{2} \right)}}$$
cot(x/4)^2*sin(x/4)^4*cot(x/2)*tan(x - asin(sin(x)/n))/(n*cot((x - asin(sin(x)/n))/2)^2*sin((x - asin(sin(x)/n))/2)^4)