Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- Общий знаменатель:
- 2/x+3+18*x/x^3+27-x+3/x^2-3*x+9
- x+4*y/12+2*x+5*y/12
- (y-20)/4*y+(5*y-2)/y^2
- 2+5*a-8/a^2-4*a+4-2*a/a-2
- cos(3*a/8)-cos(7*a/24) если a=3
- 4*z^2 если z=2
- sin(p) если p=1/2
- 18*t+t если t=-1/3
- Разложить многочлен на множители:
- A^6-1
- 10*x^2-13*x-3
- 64*m^2+16*m*y+y^2
- 5*x^2-27*x+10*x^3-125
- Умножение столбиком:
- 367*175
- 252*205
- 945*28
- 39*2345
- Деление столбиком:
- 392/6
- 407/6
- 562/6
- 916/6
- Раскрыть скобки в:
- 5*(a+b)^2-4*a^2-4*a*b
- a^4-2*(a^2+2)
- (x-4)*(x-6)*(x-10)*(x-16)*(x-25)*(x-35)*(x-50)*(x-70)*(x-95)
- 4*x*(x+6)-5*((x+6)*(x*(x+18)+216)-x*(x*(x+24)+432))
- Разложение числа на простые множители:
- 21700
- 261
- 5608
- 6465
- График функции y =:
-
2*sin(x/2+pi/6)+1
-
Идентичные выражения
- два *sin(x/ два +pi/ шесть)+ один
- 2 умножить на синус от (x делить на 2 плюс число пи делить на 6) плюс 1
- два умножить на синус от (x делить на два плюс число пи делить на шесть) плюс один
- 2sin(x/2+pi/6)+1
- 2sinx/2+pi/6+1
- 2*sin(x разделить на 2+pi разделить на 6)+1
-
Похожие выражения
- 2*sin(x/2-pi/6)+1
- 2*sin(x/2+pi/6)-1
Общий знаменатель 2*sin(x/2+pi/6)+1
Решение
Вы ввели
[src]
/x pi\
2*sin|- + --| + 1
\2 6 /
$$2 \sin{\left(\frac{x}{2} + \frac{\pi}{6} \right)} + 1$$
2*sin(x/2 + pi/6) + 1
Разложение дроби
[src]
1 + 2*sin(x/2 + pi/6)
$$2 \sin{\left(\frac{x}{2} + \frac{\pi}{6} \right)} + 1$$
/x pi\
1 + 2*sin|- + --|
\2 6 /
Объединение рациональных выражений
[src]
/pi + 3*x\
1 + 2*sin|--------|
\ 6 /
$$2 \sin{\left(\frac{3 x + \pi}{6} \right)} + 1$$
1 + 2*sin((pi + 3*x)/6)
Степени
[src]
/ / x pi\ /x pi\\
| I*|- - - --| I*|- + --||
| \ 2 6 / \2 6 /|
1 - I*\- e + e /
$$- i \left(- e^{i \left(- \frac{x}{2} - \frac{\pi}{6}\right)} + e^{i \left(\frac{x}{2} + \frac{\pi}{6}\right)}\right) + 1$$
1 - i*(-exp(i*(-x/2 - pi/6)) + exp(i*(x/2 + pi/6)))
Тригонометрическая часть
[src]
/x pi\
1 + 2*cos|- - --|
\2 3 /
$$2 \cos{\left(\frac{x}{2} - \frac{\pi}{3} \right)} + 1$$
2
1 + -----------
/x pi\
sec|- - --|
\2 3 /
$$1 + \frac{2}{\sec{\left(\frac{x}{2} - \frac{\pi}{3} \right)}}$$
2
1 + -----------
/x pi\
csc|- + --|
\2 6 /
$$1 + \frac{2}{\csc{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$$
2
1 + -------------
/ x pi\
sec|- - + --|
\ 2 3 /
$$1 + \frac{2}{\sec{\left(- \frac{x}{2} + \frac{\pi}{3} \right)}}$$
2
1 + ---------------
/ x 5*pi\
csc|- - + ----|
\ 2 6 /
$$1 + \frac{2}{\csc{\left(- \frac{x}{2} + \frac{5 \pi}{6} \right)}}$$
/x pi\
4*cot|- + --|
\4 12/
1 + ----------------
2/x pi\
1 + cot |- + --|
\4 12/
$$1 + \frac{4 \cot{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)} + 1}$$
/x pi\
4*tan|- + --|
\4 12/
1 + ----------------
2/x pi\
1 + tan |- + --|
\4 12/
$$1 + \frac{4 \tan{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)} + 1}$$
/ 2/pi x\\
2*|-1 + tan |-- + -||
\ \3 4//
1 + ---------------------
2/pi x\
1 + tan |-- + -|
\3 4/
$$\frac{2 \left(\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{3} \right)} - 1\right)}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{3} \right)} + 1} + 1$$
4
1 + ------------------------------
/ 1 \ /x pi\
|1 + ------------|*cot|- + --|
| 2/x pi\| \4 12/
| cot |- + --||
\ \4 12//
$$1 + \frac{4}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}\right) \cot{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}$$
/ 2/pi x\\
2*|1 - cot |-- + -||
\ \3 4//
1 + --------------------
2/pi x\
1 + cot |-- + -|
\3 4/
$$\frac{2 \cdot \left(- \cot^{2}{\left(\frac{x}{4} + \frac{\pi}{3} \right)} + 1\right)}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{3} \right)} + 1} + 1$$
/x pi\ /x pi\
4*sec|- + --|*sin|- + --|
\4 12/ \4 12/
1 + -------------------------
2/x pi\
1 + tan |- + --|
\4 12/
$$\frac{4 \sin{\left(\frac{x}{4} + \frac{\pi}{12} \right)} \sec{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)} + 1} + 1$$
/ x 5*pi\ /x pi\
4*csc|- - + ----|*sin|- + --|
\ 4 12 / \4 12/
1 + -----------------------------
2/x pi\
1 + tan |- + --|
\4 12/
$$\frac{4 \sin{\left(\frac{x}{4} + \frac{\pi}{12} \right)} \csc{\left(- \frac{x}{4} + \frac{5 \pi}{12} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)} + 1} + 1$$
/x pi\
4*sin|- + --|
\4 12/
1 + ------------------------------
/ 2/x pi\\ /x pi\
|1 + tan |- + --||*cos|- + --|
\ \4 12// \4 12/
$$1 + \frac{4 \sin{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)} + 1\right) \cos{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
1 + 2*|< |
|| /x pi\ |
||cos|- - --| otherwise |
\\ \2 3 / /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\cos{\left(\frac{x}{2} - \frac{\pi}{3} \right)} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
1 + 2*|< |
|| /x pi\ |
||sin|- + --| otherwise |
\\ \2 6 / /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\sin{\left(\frac{x}{2} + \frac{\pi}{6} \right)} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
1 + 2*|< 1 |
||----------- otherwise |
|| /x pi\ |
||csc|- + --| |
\\ \2 6 / /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{1}{\csc{\left(\frac{x}{2} + \frac{\pi}{6} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
1 + 2*|< 1 |
||----------- otherwise |
|| /x pi\ |
||sec|- - --| |
\\ \2 3 / /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{1}{\sec{\left(\frac{x}{2} - \frac{\pi}{3} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
2/x pi\
8*sin |- + --|
\4 12/
1 + ---------------------------------
/ 4/x pi\\
| 8*sin |- + --||
| \4 12/| /x pi\
|1 + ---------------|*sin|- + --|
| / pi\| \2 6 /
| 1 - cos|x + --||
\ \ 3 //
$$1 + \frac{8 \sin^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\left(\frac{8 \sin^{4}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{- \cos{\left(x + \frac{\pi}{3} \right)} + 1} + 1\right) \sin{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$$
2/x pi\
8*sin |- + --|
\4 12/
1 + --------------------------------
/ 4/x pi\\
| 4*sin |- + --||
| \4 12/| /x pi\
|1 + --------------|*sin|- + --|
| 2/x pi\ | \2 6 /
| sin |- + --| |
\ \2 6 / /
$$1 + \frac{8 \sin^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(\frac{x}{2} + \frac{\pi}{6} \right)}} + 1\right) \sin{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}$$
/ 5*pi x\
4*cos|- ---- + -|
\ 12 4/
1 + ----------------------------------
/ 2/ 5*pi x\\
| cos |- ---- + -||
| \ 12 4/| /x pi\
|1 + ----------------|*cos|- + --|
| 2/x pi\ | \4 12/
| cos |- + --| |
\ \4 12/ /
$$1 + \frac{4 \cos{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}}{\left(\frac{\cos^{2}{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}}{\cos^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}} + 1\right) \cos{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}$$
/x pi\
4*sec|- + --|
\4 12/
1 + --------------------------------------
/ 2/x pi\ \
| sec |- + --| |
| \4 12/ | / 5*pi x\
|1 + ----------------|*sec|- ---- + -|
| 2/ 5*pi x\| \ 12 4/
| sec |- ---- + -||
\ \ 12 4//
$$1 + \frac{4 \sec{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\sec^{2}{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}}\right) \sec{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}}$$
/ x 5*pi\
4*csc|- - + ----|
\ 4 12 /
1 + ----------------------------------
/ 2/ x 5*pi\\
| csc |- - + ----||
| \ 4 12 /| /x pi\
|1 + ----------------|*csc|- + --|
| 2/x pi\ | \4 12/
| csc |- + --| |
\ \4 12/ /
$$1 + \frac{4 \csc{\left(- \frac{x}{4} + \frac{5 \pi}{12} \right)}}{\left(\frac{\csc^{2}{\left(- \frac{x}{4} + \frac{5 \pi}{12} \right)}}{\csc^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}} + 1\right) \csc{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| /x pi\ |
1 + 2*|< 2*tan|- + --| |
|| \4 12/ |
||---------------- otherwise |
|| 2/x pi\ |
||1 + tan |- + --| |
\\ \4 12/ /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| /x pi\ |
1 + 2*|< 2*cot|- + --| |
|| \4 12/ |
||---------------- otherwise |
|| 2/x pi\ |
||1 + cot |- + --| |
\\ \4 12/ /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x 5*pi\ \
|| 1 for |- + ----| mod 2*pi = 0|
|| \2 3 / |
|| |
|| 2/pi x\ |
1 + 2*|<-1 + tan |-- + -| |
|| \3 4/ |
||----------------- otherwise |
|| 2/pi x\ |
|| 1 + tan |-- + -| |
\\ \3 4/ /
$$\left(2 \left(\begin{cases} 1 & \text{for}\: \left(\frac{x}{2} + \frac{5 \pi}{3}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{3} \right)} - 1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{3} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| 2 |
1 + 2*|<------------------------------ otherwise |
||/ 1 \ /x pi\ |
|||1 + ------------|*tan|- + --| |
||| 2/x pi\| \4 12/ |
||| tan |- + --|| |
\\\ \4 12// /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}\right) \tan{\left(\frac{x}{4} + \frac{\pi}{12} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
||/ /x pi\ |
1 + 2*|<| 0 for |- + --| mod pi = 0 |
||| \2 6 / |
||< otherwise |
||| /x pi\ |
|||sin|- + --| otherwise |
\\\ \2 6 / /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\sin{\left(\frac{x}{2} + \frac{\pi}{6} \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| /x pi\ /x pi\ |
||2*cos|- + --|*csc|- + --| |
1 + 2*|< \4 12/ \4 12/ |
||------------------------- otherwise |
|| 1 |
|| 1 + ------------ |
|| 2/x pi\ |
|| tan |- + --| |
\\ \4 12/ /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{4} + \frac{\pi}{12} \right)} \csc{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{1 + \frac{1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| /x pi\ / 5*pi x\ |
||2*cos|- + --|*sec|- ---- + -| |
1 + 2*|< \4 12/ \ 12 4/ |
||----------------------------- otherwise |
|| 1 |
|| 1 + ------------ |
|| 2/x pi\ |
|| tan |- + --| |
\\ \4 12/ /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{4} + \frac{\pi}{12} \right)} \sec{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}}{1 + \frac{1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| /x pi\ |
|| 2*cos|- + --| |
1 + 2*|< \4 12/ |
||------------------------------ otherwise |
||/ 1 \ /x pi\ |
|||1 + ------------|*sin|- + --| |
||| 2/x pi\| \4 12/ |
||| tan |- + --|| |
\\\ \4 12// /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}\right) \sin{\left(\frac{x}{4} + \frac{\pi}{12} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
||/ /x pi\ |
||| 0 for |- + --| mod pi = 0 |
||| \2 6 / |
1 + 2*|<| |
||| /x pi\ |
||< 2*cot|- + --| otherwise |
||| \4 12/ |
|||---------------- otherwise |
||| 2/x pi\ |
|||1 + cot |- + --| |
\\\ \4 12/ /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\cot^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| /x pi\ |
|| sin|- + --| |
|| \2 6 / |
1 + 2*|<--------------------------------- otherwise |
||/ 2/x pi\ \ |
||| sin |- + --| | |
||| \2 6 / | 2/x pi\ |
|||1 + --------------|*sin |- + --| |
||| 4/x pi\| \4 12/ |
||| 4*sin |- + --|| |
\\\ \4 12// /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{\sin{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{\left(1 + \frac{\sin^{2}{\left(\frac{x}{2} + \frac{\pi}{6} \right)}}{4 \sin^{4}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}\right) \sin^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| /x pi\ |
|| 2*cos|- + --| |
|| \4 12/ |
1 + 2*|<-------------------------------------- otherwise |
||/ 2/x pi\ \ |
||| cos |- + --| | |
||| \4 12/ | / 5*pi x\ |
|||1 + ----------------|*cos|- ---- + -| |
||| 2/ 5*pi x\| \ 12 4/ |
||| cos |- ---- + -|| |
\\\ \ 12 4// /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\cos^{2}{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}}\right) \cos{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| / 5*pi x\ |
|| 2*sec|- ---- + -| |
|| \ 12 4/ |
1 + 2*|<---------------------------------- otherwise |
||/ 2/ 5*pi x\\ |
||| sec |- ---- + -|| |
||| \ 12 4/| /x pi\ |
|||1 + ----------------|*sec|- + --| |
||| 2/x pi\ | \4 12/ |
||| sec |- + --| | |
\\\ \4 12/ / /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}}{\left(\frac{\sec^{2}{\left(\frac{x}{4} - \frac{5 \pi}{12} \right)}}{\sec^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}} + 1\right) \sec{\left(\frac{x}{4} + \frac{\pi}{12} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// /x pi\ \
|| 0 for |- + --| mod pi = 0|
|| \2 6 / |
|| |
|| /x pi\ |
|| 2*csc|- + --| |
|| \4 12/ |
1 + 2*|<-------------------------------------- otherwise |
||/ 2/x pi\ \ |
||| csc |- + --| | |
||| \4 12/ | / x 5*pi\ |
|||1 + ----------------|*csc|- - + ----| |
||| 2/ x 5*pi\| \ 4 12 / |
||| csc |- - + ----|| |
\\\ \ 4 12 // /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: \left(\frac{x}{2} + \frac{\pi}{6}\right) \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\left(1 + \frac{\csc^{2}{\left(\frac{x}{4} + \frac{\pi}{12} \right)}}{\csc^{2}{\left(- \frac{x}{4} + \frac{5 \pi}{12} \right)}}\right) \csc{\left(- \frac{x}{4} + \frac{5 \pi}{12} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
1 + 2*Piecewise((0, Mod(x/2 + pi/6 = pi, 0)), (2*csc(x/4 + pi/12)/((1 + csc(x/4 + pi/12)^2/csc(-x/4 + 5*pi/12)^2)*csc(-x/4 + 5*pi/12)), True))