Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- tan(x)*cos(-x)+sin(pi+x) если x=-1/2
- (a+2*b-3*c)^2 если a=2
- b^(5*sqrt(8)+1)/((b*sqrt(8))^5) если b=3/2
- a^12-b^12 если a=1
- Разложить многочлен на множители:
- 16*x^2-49
- x^3+5*x^2-3*x-15
- 121-m^2
- M^3+n^3
- Общий знаменатель:
- (15*x-11)/x-(15*t-6)/t
- 8*(sin(pi/2+t)+cos(pi+t)+sin(pi-t))/sin(t)
- 3*m/(m^2-28*m+196)-6/(m-14)
- 3/c-3-15+c/c*-9-2/c
- Умножение столбиком:
- 16*38
- 22*45
- 815*204
- 25*50
- Деление столбиком:
- 21595/7
- 749/7
- 4764/5
- 49/4
- Раскрыть скобки в:
- 3^(n+2)-2^(n+2)+3*n-2
- 2*x*2*y
- (3*a^2+5*y)*(2*a^3+y)-7*a^3*(a^2-3*y)
- (a-8)*(a+8)
- Разложение числа на простые множители:
- 7688
- 26
- 4140
- 56
- График функции y =:
- -1/2
- Интеграл d{x}:
-
-1/2
- Производная:
- -1/2
-
Идентичные выражения
- tan(x)*cos(-x)+sin(pi+x) если x=- один / два
- тангенс от (x) умножить на косинус от ( минус x) плюс синус от ( число пи плюс x) если x равно минус 1 делить на 2
- тангенс от (x) умножить на косинус от ( минус x) плюс синус от ( число пи плюс x) если x равно минус один делить на два
- tan(x)cos(-x)+sin(pi+x) если x=-1/2
- tanxcos-x+sinpi+x если x=-1/2
- tan(x)*cos(-x)+sin(pi+x) при x=-1/2
- tan(x)*cos(-x)+sin(pi+x) если x=-1 разделить на 2
-
Похожие выражения
- tan(x)*cos(x)+sin(pi+x) если x=-1/2
- tan(x)*cos(-x)-sin(pi+x) если x=-1/2
- (s-1)/2+(s-1)/2 если s=1/3
- tan(x)*cos(-x)+sin(pi+x) если x=+1/2
- tan(x)*cos(-x)+sin(pi-x) если x=-1/2
tan(x)*cos(-x)+sin(pi+x) если x=-1/2
Решение
Вы ввели
[src]
tan(x)*cos(-x) + sin(pi + x)
$$\cos{\left(- x \right)} \tan{\left(x \right)} + \sin{\left(x + \pi \right)}$$
tan(x)*cos(-x) + sin(pi + x)
Комбинаторика
[src]
-sin(x) + cos(x)*tan(x)
$$\cos{\left(x \right)} \tan{\left(x \right)} - \sin{\left(x \right)}$$
-sin(x) + cos(x)*tan(x)
Объединение рациональных выражений
[src]
-sin(x) + cos(x)*tan(x)
$$\cos{\left(x \right)} \tan{\left(x \right)} - \sin{\left(x \right)}$$
-sin(x) + cos(x)*tan(x)
Степени
[src]
-sin(x) + cos(x)*tan(x)
$$\cos{\left(x \right)} \tan{\left(x \right)} - \sin{\left(x \right)}$$
/ I*x -I*x\
|e e | / I*x -I*x\
/ I*(-pi - x) I*(pi + x)\ I*|---- + -----|*\- e + e /
I*\- e + e / \ 2 2 /
- -------------------------------- + ---------------------------------
2 I*x -I*x
e + e
$$\frac{i \left(- e^{i x} + e^{- i x}\right) \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}{e^{i x} + e^{- i x}} - \frac{i \left(- e^{i \left(- x - \pi\right)} + e^{i \left(x + \pi\right)}\right)}{2}$$
-i*(-exp(i*(-pi - x)) + exp(i*(pi + x)))/2 + i*(exp(i*x)/2 + exp(-i*x)/2)*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x))
Рациональный знаменатель
[src]
-sin(x) + cos(x)*tan(x)
$$\cos{\left(x \right)} \tan{\left(x \right)} - \sin{\left(x \right)}$$
-sin(x) + cos(x)*tan(x)
Тригонометрическая часть
[src]
0
$$0$$
-sin(x) + cos(x)*tan(x)
$$\cos{\left(x \right)} \tan{\left(x \right)} - \sin{\left(x \right)}$$
/x\
- (1 + cos(x))*tan|-| + sin(x)
\2/
$$- \left(\cos{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)} + \sin{\left(x \right)}$$
/ 2/x\\
-sin(x) + |-1 + 2*cos |-||*tan(x)
\ \2//
$$\left(2 \cos^{2}{\left(\frac{x}{2} \right)} - 1\right) \tan{\left(x \right)} - \sin{\left(x \right)}$$
/ 2/x\\
-sin(x) + |1 - 2*sin |-||*tan(x)
\ \2//
$$\left(- 2 \sin^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(x \right)} - \sin{\left(x \right)}$$
2
2*sin (x)*cos(x)
-sin(x) + ----------------
sin(2*x)
$$\frac{2 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\sin{\left(2 x \right)}} - \sin{\left(x \right)}$$
1 2*csc(2*x)
- ------ + --------------
csc(x) 2
csc (x)*sec(x)
$$- \frac{1}{\csc{\left(x \right)}} + \frac{2 \csc{\left(2 x \right)}}{\csc^{2}{\left(x \right)} \sec{\left(x \right)}}$$
2 / pi\
2*sin (x)*sin|x + --|
\ 2 /
-sin(x) + ---------------------
sin(2*x)
$$\frac{2 \sin^{2}{\left(x \right)} \sin{\left(x + \frac{\pi}{2} \right)}}{\sin{\left(2 x \right)}} - \sin{\left(x \right)}$$
2 / 2/x\\
2*sin (x)*|1 - 2*sin |-||
\ \2//
-sin(x) + -------------------------
sin(2*x)
$$\frac{2 \cdot \left(- 2 \sin^{2}{\left(\frac{x}{2} \right)} + 1\right) \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} - \sin{\left(x \right)}$$
2/ pi\
2*cos |x - --|*cos(x)
/ pi\ \ 2 /
- cos|x - --| + ---------------------
\ 2 / / pi\
cos|2*x - --|
\ 2 /
$$\frac{2 \cos{\left(x \right)} \cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(2 x - \frac{\pi}{2} \right)}} - \cos{\left(x - \frac{\pi}{2} \right)}$$
/ pi\
2*sec|2*x - --|
1 \ 2 /
- ----------- + -------------------
/ pi\ 2/ pi\
sec|x - --| sec(x)*sec |x - --|
\ 2 / \ 2 /
$$- \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} + \frac{2 \sec{\left(2 x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)} \sec^{2}{\left(x - \frac{\pi}{2} \right)}}$$
/ 2 \ /pi \
|1 - -------|*csc|-- - x|
| 2/x\| \2 /
| csc |-||
1 \ \2//
- ------ + -------------------------
csc(x) csc(x)
$$\frac{\left(1 - \frac{2}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}} - \frac{1}{\csc{\left(x \right)}}$$
/ 2/x pi\\ / pi\
|1 - 2*cos |- - --||*cos|x - --|
/ pi\ \ \2 2 // \ 2 /
- cos|x - --| + --------------------------------
\ 2 / cos(x)
$$\frac{\left(- 2 \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)} + 1\right) \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}} - \cos{\left(x - \frac{\pi}{2} \right)}$$
/ 2 \
|1 - ------------|*sec(x)
| 2/x pi\|
| sec |- - --||
1 \ \2 2 //
- ----------- + -------------------------
/ pi\ / pi\
sec|x - --| sec|x - --|
\ 2 / \ 2 /
$$\frac{\left(1 - \frac{2}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}\right) \sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}$$
/x\ / 2/x\\
2*tan|-| |1 - tan |-||*tan(x)
\2/ \ \2//
- ----------- + --------------------
2/x\ 2/x\
1 + tan |-| 1 + tan |-|
\2/ \2/
$$\frac{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(x \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
/ 2/x\ \ /x\ | 8*tan |-| | 2*tan|-| | \4/ | \2/ |1 - --------------|*tan(x) - ----------- | 2| 2/x\ | / 2/x\\ | 1 + tan |-| | |1 + tan |-|| | \2/ \ \ \4// /
$$\left(1 - \frac{8 \tan^{2}{\left(\frac{x}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}\right) \tan{\left(x \right)} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
1
1 - -------
2/x\
cot |-|
2 \2/
- -------------------- + --------------------
/ 1 \ /x\ / 1 \
|1 + -------|*cot|-| |1 + -------|*cot(x)
| 2/x\| \2/ | 2/x\|
| cot |-|| | cot |-||
\ \2// \ \2//
$$\frac{1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \cot{\left(x \right)}} - \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \cot{\left(\frac{x}{2} \right)}}$$
3
sin (x) 2/x\ 4/x\
------- - 4*sin |-|*sin(x) - 4*sin |-|*tan(x)
cos(x) \2/ \2/
---------------------------------------------
2 4/x\
sin (x) + 4*sin |-|
\2/
$$\frac{- 4 \sin^{4}{\left(\frac{x}{2} \right)} \tan{\left(x \right)} - 4 \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(x \right)} + \frac{\sin^{3}{\left(x \right)}}{\cos{\left(x \right)}}}{4 \sin^{4}{\left(\frac{x}{2} \right)} + \sin^{2}{\left(x \right)}}$$
// 0 for x mod pi = 0\ // 1 for x mod 2*pi = 0\ - |< | + |< |*tan(x) \\sin(x) otherwise / \\cos(x) otherwise /
$$\left(\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases}\right) \tan{\left(x \right)}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}\right)$$
// 0 for x mod pi = 0\ || | ||1 - cos(x) | // 1 for x mod 2*pi = 0\ - |<---------- otherwise | + |< |*tan(x) || /x\ | \\cos(x) otherwise / || tan|-| | \\ \2/ /
$$\left(\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases}\right) \tan{\left(x \right)}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{- \cos{\left(x \right)} + 1}{\tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 1 for x mod 2*pi = 0\
2 || |
2*sin (x)*|< / pi\ |
||sin|x + --| otherwise |
// 0 for x mod pi = 0\ \\ \ 2 / /
- |< | + --------------------------------------------
\\sin(x) otherwise / sin(2*x)
$$\left(\frac{2 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\sin{\left(x + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}\right)$$
/ // x \\
| || 0 for - mod pi = 0||
// 0 for x mod pi = 0\ | || 2 ||
- |< | + |1 - 2*|< ||*tan(x)
\\sin(x) otherwise / | ||1 - cos(x) ||
| ||---------- otherwise ||
\ \\ 2 //
$$\left(\left(\left(- 2 \left(\begin{cases} 0 & \text{for}\: \frac{x}{2} \bmod \pi = 0 \\\frac{- \cos{\left(x \right)} + 1}{2} & \text{otherwise} \end{cases}\right)\right) + 1\right) \tan{\left(x \right)}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}\right)$$
// 1 for x mod 2*pi = 0\ / pi\ // 0 for x mod pi = 0\ |< |*cos|x - --| || | \\cos(x) otherwise / \ 2 / - |< / pi\ | + ----------------------------------------- ||cos|x - --| otherwise | cos(x) \\ \ 2 / /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\cos{\left(x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases}\right) \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)$$
// 1 for x mod 2*pi = 0\
|| |
// 0 for x mod pi = 0\ |< 1 |*sec(x)
|| | ||------ otherwise |
|| 1 | \\sec(x) /
- |<----------- otherwise | + ------------------------------------
|| / pi\ | / pi\
||sec|x - --| | sec|x - --|
\\ \ 2 / / \ 2 /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(x \right)}} & \text{otherwise} \end{cases}\right) \sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)$$
// 1 for x mod 2*pi = 0\
|| |
|| 1 | /pi \
|<----------- otherwise |*csc|-- - x|
|| /pi \ | \2 /
// 0 for x mod pi = 0\ ||csc|-- - x| |
|| | \\ \2 / /
- |< 1 | + ----------------------------------------------
||------ otherwise | csc(x)
\\csc(x) /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{1}{\csc{\left(x \right)}} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)$$
/x\ 2/x\ / 2 \ /x pi\
2*tan|-| 8*tan |-|*\1 + tan (x)/*tan|- + --|
\2/ \2/ \2 4 /
- ----------- + ----------------------------------------
2/x\ 2
1 + tan |-| / 2/x\\ / 2/x pi\\
\2/ |1 + tan |-|| *|1 + tan |- + --||*tan(x)
\ \2// \ \2 4 //
$$- \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(\frac{x}{2} \right)} \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(x \right)}}$$
/ 1 for x mod 2*pi = 0
|
| 2/x\
|-1 + cot |-|
< \2/
// 0 for x mod pi = 0\ |------------ otherwise
|| | | 2/x\
|| /x\ | |1 + cot |-|
|| 2*cot|-| | \ \2/
- |< \2/ | + ---------------------------------
||----------- otherwise | cot(x)
|| 2/x\ |
||1 + cot |-| |
\\ \2/ /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\frac{\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}}{\cot{\left(x \right)}}\right)$$
// 0 for x mod pi = 0\ // 1 for x mod 2*pi = 0\ || | || | || /x\ | || 2/x\ | || 2*tan|-| | ||1 - tan |-| | - |< \2/ | + |< \2/ |*tan(x) ||----------- otherwise | ||----------- otherwise | || 2/x\ | || 2/x\ | ||1 + tan |-| | ||1 + tan |-| | \\ \2/ / \\ \2/ /
$$\left(\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{x}{2} \right)} + 1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \tan{\left(x \right)}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
/ 4/x\\
| 4*sin |-||
2 | \2/|
2/x\ 2*sin (x)*|1 - ---------|
4*sin |-| | 2 |
\2/ \ sin (x) /
- ---------------------- + -------------------------
/ 4/x\\ / 4/x\\
| 4*sin |-|| | 4*sin |-||
| \2/| | \2/|
|1 + ---------|*sin(x) |1 + ---------|*sin(2*x)
| 2 | | 2 |
\ sin (x) / \ sin (x) /
$$\frac{2 \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin^{2}{\left(x \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin{\left(2 x \right)}} - \frac{4 \sin^{2}{\left(\frac{x}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin{\left(x \right)}}$$
// 0 for x mod pi = 0\ // 1 for x mod 2*pi = 0\
|| | || |
- |
$$\left(\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \tan{\left(x \right)}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 1 for x mod 2*pi = 0\
|| |
// 0 for x mod pi = 0\ || 1 |
|| | ||-1 + ------- |
|| 2 | || 2/x\ |
||-------------------- otherwise | || tan |-| |
- |
$$\left(\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}} & \text{otherwise} \end{cases}\right) \tan{\left(x \right)}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// x \
|| 0 for - mod pi = 0|
|| 2 |
|| |
|| 2/x\ |
|| 4*cot |-| |
1 - 2*|< \4/ |
||-------------- otherwise |
|| 2 |
// 0 for x mod pi = 0\ ||/ 2/x\\ |
|| | |||1 + cot |-|| |
|| /x\ | ||\ \4// |
|| 2*cot|-| | \\ /
- |< \2/ | + -----------------------------------------
||----------- otherwise | cot(x)
|| 2/x\ |
||1 + cot |-| |
\\ \2/ /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(- 2 \left(\begin{cases} 0 & \text{for}\: \frac{x}{2} \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1}{\cot{\left(x \right)}}\right)$$
/ 2/x pi\\
| cos |- - --||
| \2 2 /| / pi\
|1 - ------------|*cos|x - --|
/x pi\ | 2/x\ | \ 2 /
2*cos|- - --| | cos |-| |
\2 2 / \ \2/ /
- ------------------------- + ------------------------------
/ 2/x pi\\ / 2/x pi\\
| cos |- - --|| | cos |- - --||
| \2 2 /| /x\ | \2 2 /|
|1 + ------------|*cos|-| |1 + ------------|*cos(x)
| 2/x\ | \2/ | 2/x\ |
| cos |-| | | cos |-| |
\ \2/ / \ \2/ /
$$\frac{\left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos{\left(x - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos{\left(x \right)}} - \frac{2 \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos{\left(\frac{x}{2} \right)}}$$
/ 2/x\ \
| sec |-| |
| \2/ |
|1 - ------------|*sec(x)
/x\ | 2/x pi\|
2*sec|-| | sec |- - --||
\2/ \ \2 2 //
- ------------------------------ + ------------------------------
/ 2/x\ \ / 2/x\ \
| sec |-| | | sec |-| |
| \2/ | /x pi\ | \2/ | / pi\
|1 + ------------|*sec|- - --| |1 + ------------|*sec|x - --|
| 2/x pi\| \2 2 / | 2/x pi\| \ 2 /
| sec |- - --|| | sec |- - --||
\ \2 2 // \ \2 2 //
$$\frac{\left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x \right)}}{\left(\frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}} - \frac{2 \sec{\left(\frac{x}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}$$
/ 2/pi x\\
| csc |-- - -||
| \2 2/| /pi \
|1 - ------------|*csc|-- - x|
/pi x\ | 2/x\ | \2 /
2*csc|-- - -| | csc |-| |
\2 2/ \ \2/ /
- ------------------------- + ------------------------------
/ 2/pi x\\ / 2/pi x\\
| csc |-- - -|| | csc |-- - -||
| \2 2/| /x\ | \2 2/|
|1 + ------------|*csc|-| |1 + ------------|*csc(x)
| 2/x\ | \2/ | 2/x\ |
| csc |-| | | csc |-| |
\ \2/ / \ \2/ /
$$\frac{\left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(- x + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(x \right)}} - \frac{2 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(\frac{x}{2} \right)}}$$
// 0 for x mod pi = 0\ || | || 2*sin(x) | // 1 for x mod 2*pi = 0\ ||---------------------------- otherwise | || | || / 2 \ | || 2 | - |< | sin (x) | | + |< -4 + 4*sin (x) + 4*cos(x) |*tan(x) ||(1 - cos(x))*|1 + ---------| | ||--------------------------- otherwise | || | 4/x\| | || 2 2 | || | 4*sin |-|| | \\2*(1 - cos(x)) + 2*sin (x) / || \ \2// | \\ /
$$\left(\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{4 \sin^{2}{\left(x \right)} + 4 \cos{\left(x \right)} - 4}{2 \left(- \cos{\left(x \right)} + 1\right)^{2} + 2 \sin^{2}{\left(x \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(x \right)}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \left(- \cos{\left(x \right)} + 1\right)} & \text{otherwise} \end{cases}\right)$$
/ 1 for x mod 2*pi = 0
|
|/ 1 for x mod 2*pi = 0
||
|| 2/x\
<|-1 + cot |-|
// 0 for x mod pi = 0\ |< \2/ otherwise
|| | ||------------ otherwise
||/ 0 for x mod pi = 0 | || 2/x\
||| | ||1 + cot |-|
||| /x\ | \\ \2/
- |<| 2*cot|-| | + ------------------------------------------------------
||< \2/ otherwise | cot(x)
|||----------- otherwise |
||| 2/x\ |
|||1 + cot |-| |
\\\ \2/ /
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\frac{\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}}{\cot{\left(x \right)}}\right)$$
// 1 for x mod 2*pi = 0\
|| |
|| 2 |
|| sin (x) |
||-1 + --------- |
|| 4/x\ |
2 || 4*sin |-| |
2*sin (x)*|< \2/ |
||-------------- otherwise |
|| 2 |
// 0 for x mod pi = 0\ || sin (x) |
|| | ||1 + --------- |
|| sin(x) | || 4/x\ |
||----------------------- otherwise | || 4*sin |-| |
||/ 2 \ | \\ \2/ /
- |<| sin (x) | 2/x\ | + -----------------------------------------------
|||1 + ---------|*sin |-| | sin(2*x)
||| 4/x\| \2/ |
||| 4*sin |-|| |
||\ \2// |
\\ /
$$\left(\frac{2 \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}}{1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{\sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
// 0 for x mod pi = 0\ || 0 for |x + --| mod pi = 0| // zoo for 2*x mod pi = 0\
// 0 for x mod pi = 0\ || | || \ 2 / | || |
- |< | + 2*|< 2 |*|< |*|< 1 |
\\sin(x) otherwise / ||sin (x) otherwise | || /x pi\ | ||-------- otherwise |
\\ / ||(1 + sin(x))*cot|- + --| otherwise | \\sin(2*x) /
\\ \2 4 / /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin^{2}{\left(x \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \left(x + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(x \right)} + 1\right) \cot{\left(\frac{x}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: 2 x \bmod \pi = 0 \\\frac{1}{\sin{\left(2 x \right)}} & \text{otherwise} \end{cases}\right)\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}\right)$$
// 1 for x mod 2*pi = 0\
|| |
|| 2/x\ |
|| cos |-| |
|| \2/ |
||-1 + ------------ |
|| 2/x pi\ |
|| cos |- - --| | / pi\
|< \2 2 / |*cos|x - --|
||----------------- otherwise | \ 2 /
|| 2/x\ |
// 0 for x mod pi = 0\ || cos |-| |
|| | || \2/ |
|| /x\ | || 1 + ------------ |
|| 2*cos|-| | || 2/x pi\ |
|| \2/ | || cos |- - --| |
||------------------------------ otherwise | \\ \2 2 / /
- |
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) \cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)$$
// 1 for x mod 2*pi = 0\
|| |
|| 2/x pi\ |
|| sec |- - --| |
|| \2 2 / |
||-1 + ------------ |
|| 2/x\ |
|| sec |-| |
|< \2/ |*sec(x)
||----------------- otherwise |
|| 2/x pi\ |
// 0 for x mod pi = 0\ || sec |- - --| |
|| | || \2 2 / |
|| /x pi\ | || 1 + ------------ |
|| 2*sec|- - --| | || 2/x\ |
|| \2 2 / | || sec |-| |
||------------------------- otherwise | \\ \2/ /
- |
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right) \sec{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}} & \text{otherwise} \end{cases}\right) \sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}\right)$$
// 1 for x mod 2*pi = 0\
|| |
|| 2/x\ |
|| csc |-| |
|| \2/ |
||-1 + ------------ |
|| 2/pi x\ |
|| csc |-- - -| | /pi \
|< \2 2/ |*csc|-- - x|
||----------------- otherwise | \2 /
|| 2/x\ |
// 0 for x mod pi = 0\ || csc |-| |
|| | || \2/ |
|| /x\ | || 1 + ------------ |
|| 2*csc|-| | || 2/pi x\ |
|| \2/ | || csc |-- - -| |
||------------------------------ otherwise | \\ \2 2/ /
- |
$$\left(- \begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{x}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\frac{\left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) \csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)$$
// 0 for x mod pi = 0\ // / pi\ \
// 0 for x mod pi = 0\ || | || 0 for |x + --| mod pi = 0|
|| | || 2/x\ | || \ 2 / | // zoo for 2*x mod pi = 0\
|| /x\ | || 4*cot |-| | || | || |
|| 2*cot|-| | || \2/ | || /x pi\ | || 2 |
- |< \2/ | + 2*|<-------------- otherwise |*|< 2*cot|- + --| |*|<1 + cot (x) |
||----------- otherwise | || 2 | || \2 4 / | ||----------- otherwise |
|| 2/x\ | ||/ 2/x\\ | ||---------------- otherwise | || 2*cot(x) |
||1 + cot |-| | |||1 + cot |-|| | || 2/x pi\ | \\ /
\\ \2/ / ||\ \2// | ||1 + cot |- + --| |
\\ / \\ \2 4 / /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \left(x + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: 2 x \bmod \pi = 0 \\\frac{\cot^{2}{\left(x \right)} + 1}{2 \cot{\left(x \right)}} & \text{otherwise} \end{cases}\right)\right) - \left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
-Piecewise((0, Mod(x = pi, 0)), (2*cot(x/2)/(1 + cot(x/2)^2), True)) + 2*Piecewise((0, Mod(x = pi, 0)), (4*cot(x/2)^2/(1 + cot(x/2)^2)^2, True))*Piecewise((0, Mod(x + pi/2 = pi, 0)), (2*cot(x/2 + pi/4)/(1 + cot(x/2 + pi/4)^2), True))*Piecewise((±oo, Mod(2*x = pi, 0)), ((1 + cot(x)^2)/(2*cot(x)), True))