Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- sin(a)+cos(a) если a=-2
- sin(7*y)^2-1 если y=1/4
- 5*x-12*z*(x-y)-5*y если y=3/2
- c-3/c-c*c-9/c-x/2*a если a=1/4
- Разложить многочлен на множители:
- 16*m^2-112*m+196
- 2*x+3*x^2+4*x^3
- 4*a*b+4*a*c-12*b^2-12*b*c
- z^3-1
- Общий знаменатель:
- x^2/(x-6)^2-36/(6-x)^2
- 10*(1+1)*cos(3*pi*x/4)/(pi^2*3^2)-2*(1+3)*sin(3*pi*x/4)/pi*3
- 4*x-2/(x-1)^2-3-x/(1-x)^2
- 6/1-m^2+2/m^2-3*m+2-6/m^2-m-2
- Умножение столбиком:
- 60*91
- 72*59
- 75*38
- 78*33
- Деление столбиком:
- 12000/8
- 40016/8
- 53/9
- 128/9
- Раскрыть скобки в:
- 5*(y-3)-x*(y-3)
- (a-12)*(a+12)+(a-5)^2
- p^5*(p^8*(p^4+p^7-p^11)*(p^10*p^8+p^4+p^3*p^6*p^3-p^22-p^16-p^30+p^10*p^8*p^4*p^3*p^6*p^3)+(1-p^8)*(p^4+p^7-p^11)*p^3*(p^4+p^9-p^13))+(1-p^5)*(p^8*(p^22+p^19-p^41)+(1-p^8)*p^19)
- 20*a^8*x*(9*a)^2
- Разложение числа на простые множители:
- 28600
- 24357
- 20701
- 12005
- График функции y =:
- -2
- Производная:
- -2
- Интеграл d{x}:
-
-2
-
Идентичные выражения
- sin(a)+cos(a) если a=- два
- синус от (a) плюс косинус от (a) если a равно минус 2
- синус от (a) плюс косинус от (a) если a равно минус два
- sina+cosa если a=-2
- sin(a)+cos(a) при a=-2
-
Похожие выражения
- sin(a)+cos(a) если a=+2
- sin(a)-cos(a) если a=-2
sin(a)+cos(a) если a=-2
Решение
Подстановка условия
[src]
sin(a) + cos(a) при a = -2
подставляем
sin(a) + cos(a)
$$\sin{\left(a \right)} + \cos{\left(a \right)}$$
cos(a) + sin(a)
$$\sin{\left(a \right)} + \cos{\left(a \right)}$$
переменные
a = -2
$$a = -2$$
cos((-2)) + sin((-2))
$$\sin{\left((-2) \right)} + \cos{\left((-2) \right)}$$
cos(-2) + sin(-2)
$$\sin{\left(-2 \right)} + \cos{\left(-2 \right)}$$
-sin(2) + cos(2)
$$- \sin{\left(2 \right)} + \cos{\left(2 \right)}$$
-sin(2) + cos(2)
Степени
[src]
I*a -I*a / -I*a I*a\ e e I*\- e + e / ---- + ----- - ------------------ 2 2 2
$$- \frac{i \left(e^{i a} - e^{- i a}\right)}{2} + \frac{e^{i a}}{2} + \frac{e^{- i a}}{2}$$
exp(i*a)/2 + exp(-i*a)/2 - i*(-exp(-i*a) + exp(i*a))/2
Тригонометрическая часть
[src]
___ / pi\
\/ 2 *cos|a - --|
\ 4 /
$$\sqrt{2} \cos{\left(a - \frac{\pi}{4} \right)}$$
___ / pi\
\/ 2 *sin|a + --|
\ 4 /
$$\sqrt{2} \sin{\left(a + \frac{\pi}{4} \right)}$$
___ \/ 2 ----------- / pi\ csc|a + --| \ 4 /
$$\frac{\sqrt{2}}{\csc{\left(a + \frac{\pi}{4} \right)}}$$
___ \/ 2 ----------- / pi\ sec|a - --| \ 4 /
$$\frac{\sqrt{2}}{\sec{\left(a - \frac{\pi}{4} \right)}}$$
/ pi\
cos(a) + cos|a - --|
\ 2 /
$$\cos{\left(a \right)} + \cos{\left(a - \frac{\pi}{2} \right)}$$
/ pi\
sin(a) + sin|a + --|
\ 2 /
$$\sin{\left(a \right)} + \sin{\left(a + \frac{\pi}{2} \right)}$$
1 1 ------ + ------ csc(a) sec(a)
$$\frac{1}{\sec{\left(a \right)}} + \frac{1}{\csc{\left(a \right)}}$$
2/a\
-1 + 2*cos |-| + sin(a)
\2/
$$2 \cos^{2}{\left(\frac{a}{2} \right)} + \sin{\left(a \right)} - 1$$
1 1
------ + -----------
sec(a) / pi\
sec|a - --|
\ 2 /
$$\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(a \right)}}$$
1 1
------ + -----------
sec(a) /pi \
sec|-- - a|
\2 /
$$\frac{1}{\sec{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(a \right)}}$$
1 1
------ + -----------
csc(a) /pi \
csc|-- - a|
\2 /
$$\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(a \right)}}$$
1 1
----------- + -----------
csc(pi - a) /pi \
csc|-- - a|
\2 /
$$\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- a + \pi \right)}}$$
/a\
(1 + cos(a))*tan|-| + cos(a)
\2/
$$\left(\cos{\left(a \right)} + 1\right) \tan{\left(\frac{a}{2} \right)} + \cos{\left(a \right)}$$
___ /a pi\
2*\/ 2 *tan|- + --|
\2 8 /
-------------------
2/a pi\
1 + tan |- + --|
\2 8 /
$$\frac{2 \sqrt{2} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1}$$
/ 2/a pi\\
|1 - cot |- + --||*(1 + sin(a))
\ \2 4 //
------------------------------- + cos(a)
2
$$\frac{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(a \right)} + 1\right)}{2} + \cos{\left(a \right)}$$
2/a\ /a\
1 - tan |-| 2*tan|-|
\2/ \2/
----------- + -----------
2/a\ 2/a\
1 + tan |-| 1 + tan |-|
\2/ \2/
$$\frac{- \tan^{2}{\left(\frac{a}{2} \right)} + 1}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}$$
/a\ /a pi\
2*cot|-| 2*tan|- + --|
\2/ \2 4 /
----------- + ----------------
2/a\ 2/a pi\
1 + cot |-| 1 + tan |- + --|
\2/ \2 4 /
$$\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1}$$
/a\ /a pi\
2*tan|-| 2*tan|- + --|
\2/ \2 4 /
----------- + ----------------
2/a\ 2/a pi\
1 + tan |-| 1 + tan |- + --|
\2/ \2 4 /
$$\frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}$$
2/a\ 2/a pi\
-1 + cot |-| -1 + tan |- + --|
\2/ \2 4 /
------------ + -----------------
2/a\ 2/a pi\
1 + cot |-| 1 + tan |- + --|
\2/ \2 4 /
$$\frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} + \frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}$$
2/a pi\ 2/a\
1 - cot |- + --| 1 - tan |-|
\2 4 / \2/
---------------- + -----------
2/a pi\ 2/a\
1 + cot |- + --| 1 + tan |-|
\2 4 / \2/
$$\frac{- \tan^{2}{\left(\frac{a}{2} \right)} + 1}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1}$$
1
1 - -------
2/a\
cot |-|
\2/ 2
----------- + --------------------
1 / 1 \ /a\
1 + ------- |1 + -------|*cot|-|
2/a\ | 2/a\| \2/
cot |-| | cot |-||
\2/ \ \2//
$$\frac{1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}}{1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}} + \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(\frac{a}{2} \right)}}$$
// / pi\ \
|| 0 for |a + --| mod pi = 0|
___ || \ 4 / |
\/ 2 *|< |
|| 2/a pi\ /a pi\ |
||2*sin |- + --|*cot|- + --| otherwise |
\\ \2 8 / \2 8 / /
$$\sqrt{2} \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{4}\right) \bmod \pi = 0 \\2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{8} \right)} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ |< | + |< | \\sin(a) otherwise / \\cos(a) otherwise /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 0 for |a + --| mod pi = 0|
|| \ 4 / |
|| |
___ || /a pi\ |
\/ 2 *|< 2*cot|- + --| |
|| \2 8 / |
||---------------- otherwise |
|| 2/a pi\ |
||1 + cot |- + --| |
\\ \2 8 / /
$$\sqrt{2} \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{4}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ || | // 1 for a mod 2*pi = 0\ |< / pi\ | + |< | ||cos|a - --| otherwise | \\cos(a) otherwise / \\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\cos{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right)$$
// 1 for a mod 2*pi = 0\
// 0 for a mod pi = 0\ || |
|< | + |< / pi\ |
\\sin(a) otherwise / ||sin|a + --| otherwise |
\\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\sin{\left(a + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)$$
// / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|< | + |< \ 2 / |
\\cos(a) otherwise / || |
\\sin(a) otherwise /
$$\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ || | // 1 for a mod 2*pi = 0\ || 1 | || | |<----------- otherwise | + |< 1 | || / pi\ | ||------ otherwise | ||sec|a - --| | \\sec(a) / \\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(a \right)}} & \text{otherwise} \end{cases}\right)$$
// 1 for a mod 2*pi = 0\
// 0 for a mod pi = 0\ || |
|| | || 1 |
|< 1 | + |<----------- otherwise |
||------ otherwise | || /pi \ |
\\csc(a) / ||csc|-- - a| |
\\ \2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\csc{\left(a \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ || | ||1 - cos(a) | // 1 for a mod 2*pi = 0\ |<---------- otherwise | + |< | || /a\ | \\cos(a) otherwise / || tan|-| | \\ \2/ /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{- \cos{\left(a \right)} + 1}{\tan{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right)$$
2/a\
4*sin |-|*sin(a)
2*(-1 - cos(2*a) + 2*cos(a)) \2/
------------------------------ + -------------------
2 2 4/a\
1 - cos(2*a) + 2*(1 - cos(a)) sin (a) + 4*sin |-|
\2/
$$\frac{4 \sin^{2}{\left(\frac{a}{2} \right)} \sin{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}} + \frac{2 \cdot \left(2 \cos{\left(a \right)} - \cos{\left(2 a \right)} - 1\right)}{2 \left(- \cos{\left(a \right)} + 1\right)^{2} - \cos{\left(2 a \right)} + 1}$$
4/a\
4*sin |-|
\2/
1 - --------- 2/a\
2 4*sin |-|
sin (a) \2/
------------- + ----------------------
4/a\ / 4/a\\
4*sin |-| | 4*sin |-||
\2/ | \2/|
1 + --------- |1 + ---------|*sin(a)
2 | 2 |
sin (a) \ sin (a) /
$$\frac{- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1} + \frac{4 \sin^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \sin{\left(a \right)}}$$
// / pi\ \
|| 0 for |a + --| mod pi = 0|
// 0 for a mod pi = 0\ || \ 2 / |
|< | + |< |
\\sin(a) otherwise / || /a pi\ |
||(1 + sin(a))*cot|- + --| otherwise |
\\ \2 4 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(a \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ || | || | || /a\ | || 2/a\ | || 2*cot|-| | ||-1 + cot |-| | |< \2/ | + |< \2/ | ||----------- otherwise | ||------------ otherwise | || 2/a\ | || 2/a\ | ||1 + cot |-| | ||1 + cot |-| | \\ \2/ / \\ \2/ /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 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/ /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{a}{2} \right)} + 1}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 1 |
|| | ||-1 + ------- |
|| 2 | || 2/a\ |
||-------------------- otherwise | || tan |-| |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
// 0 for a mod pi = 0\ || 0 for |a + --| mod pi = 0|
|| | || \ 2 / |
|| /a\ | || |
|| 2*cot|-| | || /a pi\ |
|< \2/ | + |< 2*cot|- + --| |
||----------- otherwise | || \2 4 / |
|| 2/a\ | ||---------------- otherwise |
||1 + cot |-| | || 2/a pi\ |
\\ \2/ / ||1 + cot |- + --| |
\\ \2 4 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
2/a pi\
cos |- - --|
\2 2 /
1 - ------------
2/a\ /a pi\
cos |-| 2*cos|- - --|
\2/ \2 2 /
---------------- + -------------------------
2/a pi\ / 2/a pi\\
cos |- - --| | cos |- - --||
\2 2 / | \2 2 /| /a\
1 + ------------ |1 + ------------|*cos|-|
2/a\ | 2/a\ | \2/
cos |-| | cos |-| |
\2/ \ \2/ /
$$\frac{1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}} + \frac{2 \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos{\left(\frac{a}{2} \right)}}$$
2/a\
sec |-|
\2/
1 - ------------
2/a pi\ /a\
sec |- - --| 2*sec|-|
\2 2 / \2/
---------------- + ------------------------------
2/a\ / 2/a\ \
sec |-| | sec |-| |
\2/ | \2/ | /a pi\
1 + ------------ |1 + ------------|*sec|- - --|
2/a pi\ | 2/a pi\| \2 2 /
sec |- - --| | sec |- - --||
\2 2 / \ \2 2 //
$$\frac{- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1}{\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1} + \frac{2 \sec{\left(\frac{a}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
2/pi a\
csc |-- - -|
\2 2/
1 - ------------
2/a\ /pi a\
csc |-| 2*csc|-- - -|
\2/ \2 2/
---------------- + -------------------------
2/pi a\ / 2/pi a\\
csc |-- - -| | csc |-- - -||
\2 2/ | \2 2/| /a\
1 + ------------ |1 + ------------|*csc|-|
2/a\ | 2/a\ | \2/
csc |-| | csc |-| |
\2/ \ \2/ /
$$\frac{1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}}{1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}} + \frac{2 \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(\frac{a}{2} \right)}}$$
// / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| | || \ 2 / |
|| 2/a\ | || |
||-1 + cot |-| | || 2/a pi\ |
|< \2/ | + |<-1 + tan |- + --| |
||------------ otherwise | || \2 4 / |
|| 2/a\ | ||----------------- otherwise |
||1 + cot |-| | || 2/a pi\ |
\\ \2/ / || 1 + tan |- + --| |
\\ \2 4 / /
$$\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ || | || 2*sin(a) | // 1 for a mod 2*pi = 0\ ||---------------------------- otherwise | || | || / 2 \ | || 2 | |< | sin (a) | | + |< -4 + 4*sin (a) + 4*cos(a) | ||(1 - cos(a))*|1 + ---------| | ||--------------------------- otherwise | || | 4/a\| | || 2 2 | || | 4*sin |-|| | \\2*(1 - cos(a)) + 2*sin (a) / || \ \2// | \\ /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \sin{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(- \cos{\left(a \right)} + 1\right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{4 \sin^{2}{\left(a \right)} + 4 \cos{\left(a \right)} - 4}{2 \left(- \cos{\left(a \right)} + 1\right)^{2} + 2 \sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right)$$
// 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/ |
|||1 + ---------|*sin |-| | ||-------------- otherwise |
||| 4/a\| \2/ | || 2 |
||| 4*sin |-|| | || sin (a) |
||\ \2// | ||1 + --------- |
\\ / || 4/a\ |
|| 4*sin |-| |
\\ \2/ /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}}{1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// 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\ | |<| 2*cot|-| | + |<|-1 + cot |-| | ||< \2/ otherwise | ||< \2/ otherwise | |||----------- otherwise | |||------------ otherwise | ||| 2/a\ | ||| 2/a\ | |||1 + cot |-| | |||1 + cot |-| | \\\ \2/ / \\\ \2/ /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 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 |- - --| |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
// 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 |-| |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \sec{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// 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 |-- - -| |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
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))