Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- m/5+3*m-m/5 если m=3/2
- 2*sin(15*x)*cos(15*x) если x=1/2
- n^4*n^(-6) если n=-4
- (1+sin(x))*(1-sin(x)) если x=1/4
- Разложить многочлен на множители:
- a^6-1
- 8*c*x^3*y-16*c^3*x^2*y
- 216+n^3
- 16*k^2+40*k*n+25*n^2
- Общий знаменатель:
- ((3-sqrt(5))/(3+sqrt(5)))+((3+sqrt(5))/(3-sqrt(5)))
- ((x^2)/(x^2+9*x*y))/x/(x^2-81*y^2)
- 2*pi/3+pi/2
- cos((3*pi/2)+a)*sin((pi/2)+a)-sin(pi-a)*cos(2*pi+a)
- Умножение столбиком:
- 48*14
- 12*45
- 23*34
- 14*60
- Деление столбиком:
- 7286/7
- 818/2
- 439/6
- 860/2
- Раскрыть скобки в:
- (x-1-i)*(x-1+i)*(x+1+i)*(x+1-i)
- (4-5*q)*(3*q-2)
- 16*a^2*c^5*(-14)*a^4*c
- 12*m-5*(2*n-(n-(1-5*n)))
- Разложение числа на простые множители:
- 2248
- 201
- 27225
- 5148
- Производная:
- 1/4
- Интеграл d{x}:
-
1/4
- График функции y =:
- 1/4
-
Идентичные выражения
- (один +sin(x))*(один -sin(x)) если x= один / четыре
- (1 плюс синус от (x)) умножить на (1 минус синус от (x)) если x равно 1 делить на 4
- (один плюс синус от (x)) умножить на (один минус синус от (x)) если x равно один делить на четыре
- (1+sin(x))(1-sin(x)) если x=1/4
- 1+sinx1-sinx если x=1/4
- (1+sin(x))*(1-sin(x)) при x=1/4
- (1+sin(x))*(1-sin(x)) если x=1 разделить на 4
-
Похожие выражения
- (1-sin(x))*(1-sin(x)) если x=1/4
- (1+sin(x))*(1+sin(x)) если x=1/4
- (1+sinx)*(1-sinx) если x=1/4
(1+sin(x))*(1-sin(x)) если x=1/4
Решение
Вы ввели
[src]
(1 + sin(x))*(1 - sin(x))
$$\left(- \sin{\left(x \right)} + 1\right) \left(\sin{\left(x \right)} + 1\right)$$
(1 + sin(x))*(1 - sin(x))
Подстановка условия
[src]
(1 + sin(x))*(1 - sin(x)) при x = 1/4
подставляем
(1 + sin(x))*(1 - sin(x))
$$\left(- \sin{\left(x \right)} + 1\right) \left(\sin{\left(x \right)} + 1\right)$$
2 cos (x)
$$\cos^{2}{\left(x \right)}$$
переменные
x = 1/4
$$x = \frac{1}{4}$$
2 cos ((1/4))
$$\cos^{2}{\left((1/4) \right)}$$
2 cos (1/4)
$$\cos^{2}{\left(\frac{1}{4} \right)}$$
cos(1/4)^2
Комбинаторика
[src]
-(1 + sin(x))*(-1 + sin(x))
$$- \left(\sin{\left(x \right)} - 1\right) \left(\sin{\left(x \right)} + 1\right)$$
-(1 + sin(x))*(-1 + sin(x))
Степени
[src]
/ / -I*x I*x\\ / / -I*x I*x\\ | I*\- e + e /| | I*\- e + e /| |1 + ------------------|*|1 - ------------------| \ 2 / \ 2 /
$$\left(- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1\right) \left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1\right)$$
(1 + i*(-exp(-i*x) + exp(i*x))/2)*(1 - i*(-exp(-i*x) + exp(i*x))/2)
Собрать выражение
[src]
1 cos(2*x) - + -------- 2 2
$$\frac{\cos{\left(2 x \right)}}{2} + \frac{1}{2}$$
1/2 + cos(2*x)/2
Тригонометрическая часть
[src]
2 cos (x)
$$\cos^{2}{\left(x \right)}$$
1 ------- 2 sec (x)
$$\frac{1}{\sec^{2}{\left(x \right)}}$$
2/ pi\
sin |x + --|
\ 2 /
$$\sin^{2}{\left(x + \frac{\pi}{2} \right)}$$
1 cos(2*x) - + -------- 2 2
$$\frac{\cos{\left(2 x \right)}}{2} + \frac{1}{2}$$
1
------------
2/pi \
csc |-- - x|
\2 /
$$\frac{1}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}$$
/ 1 \ / 1 \ |1 + ------|*|1 - ------| \ csc(x)/ \ csc(x)/
$$\left(1 - \frac{1}{\csc{\left(x \right)}}\right) \left(1 + \frac{1}{\csc{\left(x \right)}}\right)$$
/ 1 for x mod 2*pi = 0 | < 2 |cos (x) otherwise \
$$\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos^{2}{\left(x \right)} & \text{otherwise} \end{cases}$$
/ / pi\\ / / pi\\ |1 - cos|x - --||*|1 + cos|x - --|| \ \ 2 // \ \ 2 //
$$\left(- \cos{\left(x - \frac{\pi}{2} \right)} + 1\right) \left(\cos{\left(x - \frac{\pi}{2} \right)} + 1\right)$$
/ 1 \ / 1 \ |1 + -----------|*|1 - -----------| \ csc(pi - x)/ \ csc(pi - x)/
$$\left(1 - \frac{1}{\csc{\left(- x + \pi \right)}}\right) \left(1 + \frac{1}{\csc{\left(- x + \pi \right)}}\right)$$
2
/ 2/x\\
|1 - tan |-||
\ \2//
--------------
2
/ 2/x\\
|1 + tan |-||
\ \2//
$$\frac{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}$$
// 0 for x mod pi = 0\
|| |
1 - |< 2 |
||sin (x) otherwise |
\\ /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin^{2}{\left(x \right)} & \text{otherwise} \end{cases}\right) + 1$$
/ 1 \ / 1 \ |1 + -----------|*|1 - -----------| | / pi\| | / pi\| | sec|x - --|| | sec|x - --|| \ \ 2 // \ \ 2 //
$$\left(1 - \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right) \left(1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)$$
/ 1 \ / 1 \ |1 + -----------|*|1 - -----------| | /pi \| | /pi \| | sec|-- - x|| | sec|-- - x|| \ \2 // \ \2 //
$$\left(1 - \frac{1}{\sec{\left(- x + \frac{\pi}{2} \right)}}\right) \left(1 + \frac{1}{\sec{\left(- x + \frac{\pi}{2} \right)}}\right)$$
// 0 for x mod pi = 0\
|| |
1 - |<1 cos(2*x) |
||- - -------- otherwise |
\\2 2 /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\- \frac{\cos{\left(2 x \right)}}{2} + \frac{1}{2} & \text{otherwise} \end{cases}\right) + 1$$
// 0 for x mod pi = 0\
|| |
1 - |<1 1 |
||- - ---------- otherwise |
\\2 2*sec(2*x) /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{1}{2} - \frac{1}{2 \sec{\left(2 x \right)}} & \text{otherwise} \end{cases}\right) + 1$$
// 0 for x mod pi = 0\
|| |
|| /pi \ |
1 - |< sin|-- + 2*x| |
||1 \2 / |
||- - ------------- otherwise |
\\2 2 /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\- \frac{\sin{\left(2 x + \frac{\pi}{2} \right)}}{2} + \frac{1}{2} & \text{otherwise} \end{cases}\right) + 1$$
// 0 for x mod pi = 0\
|| |
||1 1 |
1 - |<- - --------------- otherwise |
||2 /pi \ |
|| 2*csc|-- - 2*x| |
\\ \2 / /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{1}{2} - \frac{1}{2 \csc{\left(- 2 x + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1$$
/ /x\\ / /x\\ |1 + (1 + cos(x))*tan|-||*|1 - (1 + cos(x))*tan|-|| \ \2// \ \2//
$$\left(- \left(\cos{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)} + 1\right) \left(\left(\cos{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)} + 1\right)$$
// / 3*pi\ \
|| 1 for |x + ----| mod 2*pi = 0|
|| \ 2 / |
1 - |< |
||1 cos(2*x) |
||- - -------- otherwise |
\\2 2 /
$$\left(- \begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\- \frac{\cos{\left(2 x \right)}}{2} + \frac{1}{2} & \text{otherwise} \end{cases}\right) + 1$$
/ /x\ \ / /x\ \ | 2*cot|-| | | 2*cot|-| | | \2/ | | \2/ | |1 - -----------|*|1 + -----------| | 2/x\| | 2/x\| | 1 + cot |-|| | 1 + cot |-|| \ \2// \ \2//
$$\left(1 - \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)$$
/ /x\ \ / /x\ \ | 2*tan|-| | | 2*tan|-| | | \2/ | | \2/ | |1 - -----------|*|1 + -----------| | 2/x\| | 2/x\| | 1 + tan |-|| | 1 + tan |-|| \ \2// \ \2//
$$\left(1 - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right) \left(1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)$$
// 0 for x mod pi = 0\
|| |
|| 2 |
1 - |<1 1 - tan (x) |
||- - --------------- otherwise |
||2 / 2 \ |
\\ 2*\1 + tan (x)/ /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\- \frac{- \tan^{2}{\left(x \right)} + 1}{2 \left(\tan^{2}{\left(x \right)} + 1\right)} + \frac{1}{2} & \text{otherwise} \end{cases}\right) + 1$$
/ 1 for x mod 2*pi = 0 | | 2 |/ 2/x\\ ||-1 + cot |-|| <\ \2// |--------------- otherwise | 2 | / 2/x\\ | |1 + cot |-|| \ \ \2//
$$\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}$$
// 0 for x mod pi = 0\
|| |
|| / 1 for x mod pi = 0 |
1 - |< < |
||1 \cos(2*x) otherwise |
||- - --------------------------- otherwise |
\\2 2 /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\left(- \frac{\begin{cases} 1 & \text{for}\: x \bmod \pi = 0 \\\cos{\left(2 x \right)} & \text{otherwise} \end{cases}}{2}\right) + \frac{1}{2} & \text{otherwise} \end{cases}\right) + 1$$
/ 2 \ / 2 \ |1 - --------------------|*|1 + --------------------| | / 1 \ /x\| | / 1 \ /x\| | |1 + -------|*cot|-|| | |1 + -------|*cot|-|| | | 2/x\| \2/| | | 2/x\| \2/| | | cot |-|| | | | cot |-|| | \ \ \2// / \ \ \2// /
$$\left(1 - \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \cot{\left(\frac{x}{2} \right)}}\right) \left(1 + \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \cot{\left(\frac{x}{2} \right)}}\right)$$
/ / 2/x pi\\ \ / / 2/x pi\\ \ | |1 - cot |- + --||*(1 + sin(x))| | |1 - cot |- + --||*(1 + sin(x))| | \ \2 4 // | | \ \2 4 // | |1 + -------------------------------|*|1 - -------------------------------| \ 2 / \ 2 /
$$\left(- \frac{\left(- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(x \right)} + 1\right)}{2} + 1\right) \left(\frac{\left(- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(x \right)} + 1\right)}{2} + 1\right)$$
/ 2/x pi\\ / 2/x pi\\ | -1 + tan |- + --|| | -1 + tan |- + --|| | \2 4 /| | \2 4 /| |1 + -----------------|*|1 - -----------------| | 2/x pi\| | 2/x pi\| | 1 + tan |- + --|| | 1 + tan |- + --|| \ \2 4 // \ \2 4 //
$$\left(- \frac{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} + 1\right) \left(\frac{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} + 1\right)$$
/ 2/x pi\\ / 2/x pi\\ | 1 - cot |- + --|| | 1 - cot |- + --|| | \2 4 /| | \2 4 /| |1 + ----------------|*|1 - ----------------| | 2/x pi\| | 2/x pi\| | 1 + cot |- + --|| | 1 + cot |- + --|| \ \2 4 // \ \2 4 //
$$\left(- \frac{- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} + 1\right) \left(\frac{- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} + 1\right)$$
// 0 for x mod pi = 0\
|| |
|| / 1 for x mod pi = 0 |
|| | |
|| | 2 |
1 - |< <-1 + cot (x) |
|| |------------ otherwise |
|| | 2 |
||1 \1 + cot (x) |
||- - ------------------------------- otherwise |
\\2 2 /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\left(- \frac{\begin{cases} 1 & \text{for}\: x \bmod \pi = 0 \\\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} & \text{otherwise} \end{cases}}{2}\right) + \frac{1}{2} & \text{otherwise} \end{cases}\right) + 1$$
/ 2/x\ \
| 4*sin |-|*sin(x) |
2 | \2/ |
(-1 + cos(x) + sin(x)) *|1 + -------------------|
| 2 4/x\|
| sin (x) + 4*sin |-||
\ \2//
-------------------------------------------------
1 2 cos(2*x)
- + (1 - cos(x)) - --------
2 2
$$\frac{\left(\frac{4 \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)} + \sin^{2}{\left(x \right)}} + 1\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)} - 1\right)^{2}}{\left(- \cos{\left(x \right)} + 1\right)^{2} - \frac{\cos{\left(2 x \right)}}{2} + \frac{1}{2}}$$
/ 2/x\ \ / 2/x\ \ | 4*sin |-| | | 4*sin |-| | | \2/ | | \2/ | |1 - ----------------------|*|1 + ----------------------| | / 4/x\\ | | / 4/x\\ | | | 4*sin |-|| | | | 4*sin |-|| | | | \2/| | | | \2/| | | |1 + ---------|*sin(x)| | |1 + ---------|*sin(x)| | | 2 | | | | 2 | | \ \ sin (x) / / \ \ sin (x) / /
$$\left(1 - \frac{4 \sin^{2}{\left(\frac{x}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin{\left(x \right)}}\right) \left(1 + \frac{4 \sin^{2}{\left(\frac{x}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin{\left(x \right)}}\right)$$
/ // 0 for x mod pi = 0\\ / // 0 for x mod pi = 0\\ | || || | || || | ||1 - cos(x) || | ||1 - cos(x) || |1 - |<---------- otherwise ||*|1 + |<---------- otherwise || | || /x\ || | || /x\ || | || tan|-| || | || tan|-| || \ \\ \2/ // \ \\ \2/ //
$$\left(\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{- \cos{\left(x \right)} + 1}{\tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{- \cos{\left(x \right)} + 1}{\tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right)$$
/ // 0 for x mod pi = 0\\ / // 0 for x mod pi = 0\\ | || || | || || | || /x\ || | || /x\ || | || 2*cot|-| || | || 2*cot|-| || |1 - |< \2/ ||*|1 + |< \2/ || | ||----------- otherwise || | ||----------- otherwise || | || 2/x\ || | || 2/x\ || | ||1 + cot |-| || | ||1 + cot |-| || \ \\ \2/ // \ \\ \2/ //
$$\left(\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + 1\right)$$
/ // 0 for x mod pi = 0\\ / // 0 for x mod pi = 0\\
| || || | || ||
| || 2 || | || 2 ||
| ||-------------------- otherwise || | ||-------------------- otherwise ||
|1 - |
$$\left(\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right)$$
/ /x pi\ \ / /x pi\ \ | 2*cos|- - --| | | 2*cos|- - --| | | \2 2 / | | \2 2 / | |1 - -------------------------|*|1 + -------------------------| | / 2/x pi\\ | | / 2/x pi\\ | | | cos |- - --|| | | | cos |- - --|| | | | \2 2 /| /x\| | | \2 2 /| /x\| | |1 + ------------|*cos|-|| | |1 + ------------|*cos|-|| | | 2/x\ | \2/| | | 2/x\ | \2/| | | cos |-| | | | | cos |-| | | \ \ \2/ / / \ \ \2/ / /
$$\left(1 - \frac{2 \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos{\left(\frac{x}{2} \right)}}\right) \left(1 + \frac{2 \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos{\left(\frac{x}{2} \right)}}\right)$$
/ /x\ \ / /x\ \ | 2*sec|-| | | 2*sec|-| | | \2/ | | \2/ | |1 - ------------------------------|*|1 + ------------------------------| | / 2/x\ \ | | / 2/x\ \ | | | sec |-| | | | | sec |-| | | | | \2/ | /x pi\| | | \2/ | /x pi\| | |1 + ------------|*sec|- - --|| | |1 + ------------|*sec|- - --|| | | 2/x pi\| \2 2 /| | | 2/x pi\| \2 2 /| | | sec |- - --|| | | | sec |- - --|| | \ \ \2 2 // / \ \ \2 2 // /
$$\left(1 - \frac{2 \sec{\left(\frac{x}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}\right) \left(1 + \frac{2 \sec{\left(\frac{x}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}\right)$$
/ /pi x\ \ / /pi x\ \ | 2*csc|-- - -| | | 2*csc|-- - -| | | \2 2/ | | \2 2/ | |1 - -------------------------|*|1 + -------------------------| | / 2/pi x\\ | | / 2/pi x\\ | | | csc |-- - -|| | | | csc |-- - -|| | | | \2 2/| /x\| | | \2 2/| /x\| | |1 + ------------|*csc|-|| | |1 + ------------|*csc|-|| | | 2/x\ | \2/| | | 2/x\ | \2/| | | csc |-| | | | | csc |-| | | \ \ \2/ / / \ \ \2/ / /
$$\left(1 - \frac{2 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(\frac{x}{2} \right)}}\right) \left(1 + \frac{2 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(\frac{x}{2} \right)}}\right)$$
/ // / 3*pi\ \\ / // / 3*pi\ \\ | || 1 for |x + ----| mod 2*pi = 0|| | || 1 for |x + ----| mod 2*pi = 0|| | || \ 2 / || | || \ 2 / || | || || | || || | || 2/x pi\ || | || 2/x pi\ || |1 - |<-1 + tan |- + --| ||*|1 + |<-1 + tan |- + --| || | || \2 4 / || | || \2 4 / || | ||----------------- otherwise || | ||----------------- otherwise || | || 2/x pi\ || | || 2/x pi\ || | || 1 + tan |- + --| || | || 1 + tan |- + --| || \ \\ \2 4 / // \ \\ \2 4 / //
$$\left(\left(- \begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + 1\right)$$
/ // 0 for x mod pi = 0\\ / // 0 for x mod pi = 0\\ | || || | || || | || sin(x) || | || sin(x) || | ||----------------------- otherwise || | ||----------------------- otherwise || | ||/ 2 \ || | ||/ 2 \ || |1 - |<| sin (x) | 2/x\ ||*|1 + |<| sin (x) | 2/x\ || | |||1 + ---------|*sin |-| || | |||1 + ---------|*sin |-| || | ||| 4/x\| \2/ || | ||| 4/x\| \2/ || | ||| 4*sin |-|| || | ||| 4*sin |-|| || | ||\ \2// || | ||\ \2// || \ \\ // \ \\ //
$$\left(\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{\sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{\sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right)$$
/ // 0 for x mod pi = 0\\ / // 0 for x mod pi = 0\\ | || || | || || | || 2*sin(x) || | || 2*sin(x) || | ||---------------------------- otherwise || | ||---------------------------- otherwise || | || / 2 \ || | || / 2 \ || |1 - |< | sin (x) | ||*|1 + |< | sin (x) | || | ||(1 - cos(x))*|1 + ---------| || | ||(1 - cos(x))*|1 + ---------| || | || | 4/x\| || | || | 4/x\| || | || | 4*sin |-|| || | || | 4*sin |-|| || | || \ \2// || | || \ \2// || \ \\ // \ \\ //
$$\left(\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \left(- \cos{\left(x \right)} + 1\right)} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \left(- \cos{\left(x \right)} + 1\right)} & \text{otherwise} \end{cases}\right) + 1\right)$$
/ // 0 for x mod pi = 0\\ / // 0 for x mod pi = 0\\
| || || | || ||
| || /x pi\ || | || /x pi\ ||
| || 2*sec|- - --| || | || 2*sec|- - --| ||
| || \2 2 / || | || \2 2 / ||
| ||------------------------- otherwise || | ||------------------------- otherwise ||
|1 - |
$$\left(\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right) \sec{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right) \sec{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right)$$
/ // 0 for x mod pi = 0\\ / // 0 for x mod pi = 0\\
| || || | || ||
| || /x\ || | || /x\ ||
| || 2*cos|-| || | || 2*cos|-| ||
| || \2/ || | || \2/ ||
| ||------------------------------ otherwise || | ||------------------------------ otherwise ||
|1 - |
$$\left(\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right)$$
/ // 0 for x mod pi = 0\\ / // 0 for x mod pi = 0\\
| || || | || ||
| || /x\ || | || /x\ ||
| || 2*csc|-| || | || 2*csc|-| ||
| || \2/ || | || \2/ ||
| ||------------------------------ otherwise || | ||------------------------------ otherwise ||
|1 - |
$$\left(\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{x}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right) \left(\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{x}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1\right)$$
(1 - Piecewise((0, Mod(x = pi, 0)), (2*csc(x/2)/((1 + csc(x/2)^2/csc(pi/2 - x/2)^2)*csc(pi/2 - x/2)), True)))*(1 + Piecewise((0, Mod(x = pi, 0)), (2*csc(x/2)/((1 + csc(x/2)^2/csc(pi/2 - x/2)^2)*csc(pi/2 - x/2)), True)))