Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- sin(a)*cos(a)*cot(a)-1 если a=-2
- (5-c)*(5+c)+c2 если c2=-4
- (b-7)*(b+7) если b=-4
- x^2 если x=-2
- Разложить многочлен на множители:
- x^2-64
- a^3-27
- 64-x^3*y^6
- 6*x^2-24
- Общий знаменатель:
- c^2/(c^2-16)-c/(c+4)
- y/4+(y-2)/5
- 2*m-4*n/21*c+5*m+18*n/21*c
- 2/a^2-9-1/a^2+3*a
- Умножение столбиком:
- 35*35
- 81*81
- 34*12
- 12*25
- Деление столбиком:
- 391/3
- 55/3
- 84/3
- 54/4
- Раскрыть скобки в:
- (a-b-c)*(a-b+c)
- (x+5)*(y-7)
- (x-2)*(x^2+2*x+4)
- (m^3*m^4)^2*(2*m)^3
- Разложение числа на простые множители:
- 2772
- 756
- 1848
- 2002
- График функции y =:
- -2
- Производная:
- -2
- Интеграл d{x}:
-
-2
-
Идентичные выражения
- sin(a)*cos(a)*cot(a)- один если a=- два
- синус от (a) умножить на косинус от (a) умножить на котангенс от (a) минус 1 если a равно минус 2
- синус от (a) умножить на косинус от (a) умножить на котангенс от (a) минус один если a равно минус два
- sin(a)cos(a)cot(a)-1 если a=-2
- sinacosacota-1 если a=-2
- sin(a)*cos(a)*cot(a)-1 при a=-2
-
Похожие выражения
- sin(a)*cos(a)*cot(a)-1 если a=+2
- sin(a)*cos(a)*cot(a)+1 если a=-2
sin(a)*cos(a)*cot(a)-1 если a=-2
Решение
Вы ввели
[src]
sin(a)*cos(a)*cot(a) - 1
$$\sin{\left(a \right)} \cos{\left(a \right)} \cot{\left(a \right)} - 1$$
sin(a)*cos(a)*cot(a) - 1*1
Подстановка условия
[src]
sin(a)*cos(a)*cot(a) - 1*1 при a = -2
подставляем
sin(a)*cos(a)*cot(a) - 1
$$\sin{\left(a \right)} \cos{\left(a \right)} \cot{\left(a \right)} - 1$$
2 -sin (a)
$$- \sin^{2}{\left(a \right)}$$
переменные
a = -2
$$a = -2$$
2 -sin ((-2))
$$- \sin^{2}{\left((-2) \right)}$$
2 -sin (-2)
$$- \sin^{2}{\left(-2 \right)}$$
2 -sin (2)
$$- \sin^{2}{\left(2 \right)}$$
-sin(2)^2
Степени
[src]
/ I*a -I*a\
|e e | / -I*a I*a\
I*|---- + -----|*\- e + e /*cot(a)
\ 2 2 /
-1 - ----------------------------------------
2
$$- \frac{i \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right) \left(e^{i a} - e^{- i a}\right) \cot{\left(a \right)}}{2} - 1$$
-1 - i*(exp(i*a)/2 + exp(-i*a)/2)*(-exp(-i*a) + exp(i*a))*cot(a)/2
Собрать выражение
[src]
1 cos(2*a) - - + -------- 2 2
$$\frac{\cos{\left(2 a \right)}}{2} - \frac{1}{2}$$
-1/2 + cos(2*a)/2
Тригонометрическая часть
[src]
2 -sin (a)
$$- \sin^{2}{\left(a \right)}$$
2 -1 + cos (a)
$$\cos^{2}{\left(a \right)} - 1$$
-1 ------- 2 csc (a)
$$- \frac{1}{\csc^{2}{\left(a \right)}}$$
1
-1 + -------
2
sec (a)
$$-1 + \frac{1}{\sec^{2}{\left(a \right)}}$$
2/ pi\
-cos |a - --|
\ 2 /
$$- \cos^{2}{\left(a - \frac{\pi}{2} \right)}$$
1
-1 + -----------
2
1 + tan (a)
$$-1 + \frac{1}{\tan^{2}{\left(a \right)} + 1}$$
2/ pi\
-1 + sin |a + --|
\ 2 /
$$\sin^{2}{\left(a + \frac{\pi}{2} \right)} - 1$$
1 cos(2*a) - - + -------- 2 2
$$\frac{\cos{\left(2 a \right)}}{2} - \frac{1}{2}$$
-1
------------
2/ pi\
sec |a - --|
\ 2 /
$$- \frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$
1
-1 + ------------
2/pi \
csc |-- - a|
\2 /
$$-1 + \frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}$$
sin(2*a)
-1 + --------
2*tan(a)
$$\frac{\sin{\left(2 a \right)}}{2 \tan{\left(a \right)}} - 1$$
2
sin (2*a)
-1 + ---------
2
4*sin (a)
$$-1 + \frac{\sin^{2}{\left(2 a \right)}}{4 \sin^{2}{\left(a \right)}}$$
cos(a)*sin(2*a)
-1 + ---------------
2*sin(a)
$$\frac{\sin{\left(2 a \right)} \cos{\left(a \right)}}{2 \sin{\left(a \right)}} - 1$$
csc(a)
-1 + -----------------
2*csc(2*a)*sec(a)
$$-1 + \frac{\csc{\left(a \right)}}{2 \csc{\left(2 a \right)} \sec{\left(a \right)}}$$
2/a\ / 2/a\\
4*cos |-|*|-1 + cos |-||
\2/ \ \2//
$$4 \left(\cos^{2}{\left(\frac{a}{2} \right)} - 1\right) \cos^{2}{\left(\frac{a}{2} \right)}$$
/ pi\
sin(2*a)*sin|a + --|
\ 2 /
-1 + --------------------
2*sin(a)
$$\frac{\sin{\left(2 a \right)} \sin{\left(a + \frac{\pi}{2} \right)}}{2 \sin{\left(a \right)}} - 1$$
csc(a)
-1 + ----------------------
/pi \
2*csc(2*a)*csc|-- - a|
\2 /
$$-1 + \frac{\csc{\left(a \right)}}{2 \csc{\left(2 a \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}$$
2/a\
-4*tan |-|
\2/
--------------
2
/ 2/a\\
|1 + tan |-||
\ \2//
$$- \frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
// 0 for a mod pi = 0\ || | -|< 2 | ||sin (a) otherwise | \\ /
$$- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}$$
/ pi\
cos(a)*cos|2*a - --|
\ 2 /
-1 + --------------------
/ pi\
2*cos|a - --|
\ 2 /
$$\frac{\cos{\left(a \right)} \cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos{\left(a - \frac{\pi}{2} \right)}} - 1$$
/ pi\
sec|a - --|
\ 2 /
-1 + ----------------------
/ pi\
2*sec(a)*sec|2*a - --|
\ 2 /
$$-1 + \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{2 \sec{\left(a \right)} \sec{\left(2 a - \frac{\pi}{2} \right)}}$$
// 1 for a mod 2*pi = 0\
|| |
-1 + |< 2 |
||cos (a) otherwise |
\\ /
$$\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) - 1$$
2
/ 2/a\\
|-1 + cot |-||
\ \2//
-1 + ---------------
2
/ 2/a\\
|1 + cot |-||
\ \2//
$$\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - 1$$
2
/ 2/a\\
|1 - tan |-||
\ \2//
-1 + --------------
2
/ 2/a\\
|1 + tan |-||
\ \2//
$$\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - 1$$
2 /a\
cos (a)*(1 + cos(a))*tan|-|
\2/
-1 + ---------------------------
sin(a)
$$\frac{\left(\cos{\left(a \right)} + 1\right) \cos^{2}{\left(a \right)} \tan{\left(\frac{a}{2} \right)}}{\sin{\left(a \right)}} - 1$$
2/a pi\
4*tan |- + --|
\2 4 /
-1 + -------------------
2
/ 2/a pi\\
|1 + tan |- + --||
\ \2 4 //
$$-1 + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$
// 0 for 2*a mod pi = 0\
|< |*cot(a)
\\sin(2*a) otherwise /
-1 + --------------------------------------
2
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\sin{\left(2 a \right)} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)}}{2}\right) - 1$$
// 0 for a mod pi = 0\ || | || 2/a\ | || 4*cot |-| | || \2/ | -|<-------------- otherwise | || 2 | ||/ 2/a\\ | |||1 + cot |-|| | ||\ \2// | \\ /
$$- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}$$
/ 2/a\\ /a\
2*|1 - tan |-||*tan|-|
\ \2// \2/
-1 + ----------------------
2
/ 2/a\\
|1 + tan |-|| *tan(a)
\ \2//
$$-1 + \frac{2 \cdot \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)}}$$
/ 1 \
2*|1 - -------|*cot(a)
| 2/a\|
| cot |-||
\ \2//
-1 + ----------------------
2
/ 1 \ /a\
|1 + -------| *cot|-|
| 2/a\| \2/
| cot |-||
\ \2//
$$-1 + \frac{2 \cdot \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(a \right)}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cot{\left(\frac{a}{2} \right)}}$$
// 0 for 2*a mod pi = 0\
|| |
|| 2*cot(a) |
|<----------- otherwise |*cot(a)
|| 2 |
||1 + cot (a) |
\\ /
-1 + -----------------------------------------
2
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)}}{2}\right) - 1$$
// 1 for a mod 2*pi = 0\
|| |
|| 2 |
||/ 2/a\\ |
|||-1 + cot |-|| |
-1 + |<\ \2// |
||--------------- otherwise |
|| 2 |
|| / 2/a\\ |
|| |1 + cot |-|| |
\\ \ \2// /
$$\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
2/a\ / 2 4/a\\
4*sin |-|*|sin (a) - 4*sin |-||*cos(a)
\2/ \ \2//
-1 + --------------------------------------
2
/ 2 4/a\\
|sin (a) + 4*sin |-||
\ \2//
$$\frac{4 \left(- 4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right) \sin^{2}{\left(\frac{a}{2} \right)} \cos{\left(a \right)}}{\left(4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}} - 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
-1 + |< |*|< |*cot(a)
\\sin(a) otherwise / \\cos(a) otherwise /
$$\left(\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)}\right) - 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|< |*|< |
\\sin(a) otherwise / \\cos(a) otherwise /
-1 + ---------------------------------------------------------
tan(a)
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right)}{\tan{\left(a \right)}}\right) - 1$$
/ 2/a\\ /a pi\
|1 + tan |-||*tan(a)*tan|- + --|
\ \2// \2 4 /
-1 + ---------------------------------------
/ 2 \ / 2/a pi\\ /a\
\1 + tan (a)/*|1 + tan |- + --||*tan|-|
\ \2 4 // \2/
$$\frac{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(a \right)} + 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)}} - 1$$
/ 4/a\\
| 4*sin |-||
2/a\ | \2/|
2*sin |-|*|1 - ---------|*sin(2*a)
\2/ | 2 |
\ sin (a) /
-1 + ----------------------------------
2
/ 4/a\\
| 4*sin |-||
| \2/| 3
|1 + ---------| *sin (a)
| 2 |
\ sin (a) /
$$-1 + \frac{2 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin{\left(2 a \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2} \sin^{3}{\left(a \right)}}$$
// 1 for a mod 2*pi = 0\
// 0 for a mod pi = 0\ || |
|< |*|< / pi\ |*sin(2*a)
\\sin(a) otherwise / ||sin|a + --| otherwise |
\\ \ 2 / /
-1 + -----------------------------------------------------------------------
2
2*sin (a)
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\sin{\left(a + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}}\right) - 1$$
// 0 for a mod pi = 0\
|| |
||1 - cos(a) | // 1 for a mod 2*pi = 0\
|<---------- otherwise |*|< |
|| /a\ | \\cos(a) otherwise /
|| tan|-| |
\\ \2/ /
-1 + -------------------------------------------------------------
tan(a)
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{- \cos{\left(a \right)} + 1}{\tan{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right)}{\tan{\left(a \right)}}\right) - 1$$
// 0 for a mod pi = 0\
|| | // 1 for a mod 2*pi = 0\
|< / pi\ |*|< |*cos(a)
||cos|a - --| otherwise | \\cos(a) otherwise /
\\ \ 2 / /
-1 + ---------------------------------------------------------------------
/ pi\
cos|a - --|
\ 2 /
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\cos{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}}\right) - 1$$
// 0 for a mod pi = 0\
|| | // 1 for a mod 2*pi = 0\
|| 1 | || | / pi\
|<----------- otherwise |*|< 1 |*sec|a - --|
|| / pi\ | ||------ otherwise | \ 2 /
||sec|a - --| | \\sec(a) /
\\ \ 2 / /
-1 + --------------------------------------------------------------------------
sec(a)
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(a \right)}} & \text{otherwise} \end{cases}\right) \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}\right) - 1$$
// 1 for a mod 2*pi = 0\
// 0 for a mod pi = 0\ || |
|| | || 1 |
|< 1 |*|<----------- otherwise |*csc(a)
||------ otherwise | || /pi \ |
\\csc(a) / ||csc|-- - a| |
\\ \2 / /
-1 + ---------------------------------------------------------------------
/pi \
csc|-- - a|
\2 /
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\csc{\left(a \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}}\right) - 1$$
/ 2/a\ \
| sec |-| |
| \2/ | /a\ / pi\
2*|1 - ------------|*sec|-|*sec|a - --|
| 2/a pi\| \2/ \ 2 /
| sec |- - --||
\ \2 2 //
-1 + ---------------------------------------
2
/ 2/a\ \
| sec |-| |
| \2/ | /a pi\
|1 + ------------| *sec(a)*sec|- - --|
| 2/a pi\| \2 2 /
| sec |- - --||
\ \2 2 //
$$-1 + \frac{2 \left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{a}{2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \sec{\left(a \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
/ 2/a pi\\
| cos |- - --||
| \2 2 /| /a pi\
2*|1 - ------------|*cos(a)*cos|- - --|
| 2/a\ | \2 2 /
| cos |-| |
\ \2/ /
-1 + ---------------------------------------
2
/ 2/a pi\\
| cos |- - --||
| \2 2 /| /a\ / pi\
|1 + ------------| *cos|-|*cos|a - --|
| 2/a\ | \2/ \ 2 /
| cos |-| |
\ \2/ /
$$-1 + \frac{2 \cdot \left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos{\left(a \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cos{\left(\frac{a}{2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| /a\ | || 2/a\ |
|| 2*cot|-| | ||-1 + cot |-| |
-1 + |< \2/ |*|< \2/ |*cot(a)
||----------- otherwise | ||------------ otherwise |
|| 2/a\ | || 2/a\ |
||1 + cot |-| | ||1 + cot |-| |
\\ \2/ / \\ \2/ /
$$\left(\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)}\right) - 1$$
/ 2/pi a\\
| csc |-- - -||
| \2 2/| /pi a\
2*|1 - ------------|*csc(a)*csc|-- - -|
| 2/a\ | \2 2/
| csc |-| |
\ \2/ /
-1 + ---------------------------------------
2
/ 2/pi a\\
| csc |-- - -||
| \2 2/| /a\ /pi \
|1 + ------------| *csc|-|*csc|-- - a|
| 2/a\ | \2/ \2 /
| csc |-| |
\ \2/ /
$$-1 + \frac{2 \cdot \left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(a \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \csc{\left(\frac{a}{2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| /a\ | || 2/a\ |
|| 2*tan|-| | ||1 - tan |-| |
|< \2/ |*|< \2/ |
||----------- otherwise | ||----------- otherwise |
|| 2/a\ | || 2/a\ |
||1 + tan |-| | ||1 + tan |-| |
\\ \2/ / \\ \2/ /
-1 + -------------------------------------------------------------------
tan(a)
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{a}{2} \right)} + 1}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)}{\tan{\left(a \right)}}\right) - 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
-1 + |
$$\left(\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)}\right) - 1$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 1 |
|| | ||-1 + ------- |
|| 2 | || 2/a\ |
||-------------------- otherwise | || tan |-| |
|
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}} & \text{otherwise} \end{cases}\right)}{\tan{\left(a \right)}}\right) - 1$$
// / pi\ \
|| 0 for |a + --| mod pi = 0| // zoo for a mod pi = 0\
// 0 for 2*a mod pi = 0\ || \ 2 / | || |
|< |*|< |*|< 1 |
\\sin(2*a) otherwise / || /a pi\ | ||------ otherwise |
||(1 + sin(a))*cot|- + --| otherwise | \\sin(a) /
\\ \2 4 / /
-1 + ----------------------------------------------------------------------------------------------------------------
2
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\sin{\left(2 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(a \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sin{\left(a \right)}} & \text{otherwise} \end{cases}\right)}{2}\right) - 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| -2*sin(2*a) + 4*sin(a) | || -2 - 2*cos(2*a) + 4*cos(a) |
|<------------------------------ otherwise |*|<------------------------------ otherwise |
|| 2 | || 2 |
||1 - cos(2*a) + 2*(1 - cos(a)) | ||1 - cos(2*a) + 2*(1 - cos(a)) |
\\ / \\ /
-1 + ---------------------------------------------------------------------------------------------------------
tan(a)
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \sin{\left(a \right)} - 2 \sin{\left(2 a \right)}}{2 \left(- \cos{\left(a \right)} + 1\right)^{2} - \cos{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{4 \cos{\left(a \right)} - 2 \cos{\left(2 a \right)} - 2}{2 \left(- \cos{\left(a \right)} + 1\right)^{2} - \cos{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right)}{\tan{\left(a \right)}}\right) - 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
||/ 0 for a mod pi = 0 | ||/ 1 for a mod 2*pi = 0 |
||| | ||| |
||| /a\ | ||| 2/a\ |
-1 + |<| 2*cot|-| |*|<|-1 + cot |-| |*cot(a)
||< \2/ otherwise | ||< \2/ otherwise |
|||----------- otherwise | |||------------ otherwise |
||| 2/a\ | ||| 2/a\ |
|||1 + cot |-| | |||1 + cot |-| |
\\\ \2/ / \\\ \2/ /
$$\left(\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \cot{\left(a \right)}\right) - 1$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | || sin (a) |
|| sin(a) | ||-1 + --------- |
||----------------------- otherwise | || 4/a\ |
||/ 2 \ | || 4*sin |-| |
|<| sin (a) | 2/a\ |*|< \2/ |*sin(2*a)
|||1 + ---------|*sin |-| | ||-------------- otherwise |
||| 4/a\| \2/ | || 2 |
||| 4*sin |-|| | || sin (a) |
||\ \2// | ||1 + --------- |
\\ / || 4/a\ |
|| 4*sin |-| |
\\ \2/ /
-1 + -------------------------------------------------------------------------------------------
2
2*sin (a)
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}}{1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}} & \text{otherwise} \end{cases}\right) \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}}\right) - 1$$
// / pi\ \
|| 0 for |a + --| mod pi = 0| // zoo for a mod pi = 0\
// 0 for 2*a mod pi = 0\ || \ 2 / | || |
|| | || | || 2/a\ |
|| 2*cot(a) | || /a pi\ | ||1 + cot |-| |
|<----------- otherwise |*|< 2*cot|- + --| |*|< \2/ |
|| 2 | || \2 4 / | ||----------- otherwise |
||1 + cot (a) | ||---------------- otherwise | || /a\ |
\\ / || 2/a pi\ | || 2*cot|-| |
||1 + cot |- + --| | \\ \2/ /
\\ \2 4 / /
-1 + ----------------------------------------------------------------------------------------------------------------
2
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: a \bmod \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} \right)} + 1}{2 \cot{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)}{2}\right) - 1$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2/a\ |
|| | || cos |-| |
|| /a\ | || \2/ |
|| 2*cos|-| | ||-1 + ------------ |
|| \2/ | || 2/a pi\ |
||------------------------------ otherwise | || cos |- - --| |
|
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}}\right) - 1$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2/a pi\ |
|| | || sec |- - --| |
|| /a pi\ | || \2 2 / |
|| 2*sec|- - --| | ||-1 + ------------ |
|| \2 2 / | || 2/a\ |
||------------------------- otherwise | || sec |-| | / pi\
|
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \sec{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}} & \text{otherwise} \end{cases}\right) \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}\right) - 1$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2/a\ |
|| | || csc |-| |
|| /a\ | || \2/ |
|| 2*csc|-| | ||-1 + ------------ |
|| \2/ | || 2/pi a\ |
||------------------------------ otherwise | || csc |-- - -| |
|
$$\left(\frac{\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}}\right) - 1$$
-1 + Piecewise((0, Mod(a = pi, 0)), (2*csc(a/2)/((1 + csc(a/2)^2/csc(pi/2 - a/2)^2)*csc(pi/2 - a/2)), True))*Piecewise((1, Mod(a = 2*pi, 0)), ((-1 + csc(a/2)^2/csc(pi/2 - a/2)^2)/(1 + csc(a/2)^2/csc(pi/2 - a/2)^2), True))*csc(a)/csc(pi/2 - a)