Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- 4*cos(a)^2+4*sin(a)^2 если a=-4
- 8+x+13+x если x=3
- 1/(sin(x)^2)-1 если x=-1/4
- k-(-1)*k-4+16-k если k=4
- Разложить многочлен на множители:
- x^3-6*x^2+11*x-6
- 8/27+z^3
- 10*x^3-2*x^2*y+15*x^2*z-3*x*y*z
- x^4-9*x^3+x^2+81*x+70
- Общий знаменатель:
- (((sqrt(q))/(p-sqrt(p*q)))+((sqrt(p))/(q-sqrt(p*q))))*((p*sqrt(q)+q*sqrt(p))/(p-q))
- 1/b*(a*b*c+a+c)-(1/a+(1/(b+1/c)))/(1/(a+1/b))
- cos(pi/2+a)*sin(pi+a)+tan(3*pi/2+a)*sin(a-pi/2)*cos(pi/2-a)
- (8*(sin((pi/2)+x)+cos(pi+x)+sin(pi-x)))/sin(x)
- Умножение столбиком:
- 74*28
- 805*119
- 5702*37
- 32*22
- Деление столбиком:
- 544/3
- 1215/3
- 227/5
- 676/5
- Раскрыть скобки в:
- (y-4)*2-(4-y)*(4+y)
- x^(n-1)*(x^(n-6)-1)-x^(n+2)*(x^(n+5)-x^3)
- x^(2*n)-9
- (2*a+5)^2-3*(a-7)*(7-a)+9*a^2-79
- Разложение числа на простые множители:
- 2756
- 36142
- 86220
- 54756
- Производная:
- -4
- Интеграл d{x}:
-
-4
- График функции y =:
- -4
-
Идентичные выражения
- четыре *cos(a)^ два + четыре *sin(a)^ два если a=- четыре
- 4 умножить на косинус от (a) в квадрате плюс 4 умножить на синус от (a) в квадрате если a равно минус 4
- четыре умножить на косинус от (a) в степени два плюс четыре умножить на синус от (a) в степени два если a равно минус четыре
- 4*cos(a)2+4*sin(a)2 если a=-4
- 4*cosa2+4*sina2 если a=-4
- 4*cos(a)²+4*sin(a)² если a=-4
- 4*cos(a) в степени 2+4*sin(a) в степени 2 если a=-4
- 4cos(a)^2+4sin(a)^2 если a=-4
- 4cos(a)2+4sin(a)2 если a=-4
- 4cosa2+4sina2 если a=-4
- 4cosa^2+4sina^2 если a=-4
- 4*cos(a)^2+4*sin(a)^2 при a=-4
-
Похожие выражения
- 4*cos(a)^2+4*sin(a)^2 если a=+4
- 4*cos(a)^2-4*sin(a)^2 если a=-4
4*cos(a)^2+4*sin(a)^2 если a=-4
Решение
Вы ввели
[src]
2 2 4*cos (a) + 4*sin (a)
$$4 \sin^{2}{\left(a \right)} + 4 \cos^{2}{\left(a \right)}$$
4*cos(a)^2 + 4*sin(a)^2
Объединение рациональных выражений
[src]
/ 2 2 \ 4*\cos (a) + sin (a)/
$$4 \left(\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}\right)$$
4*(cos(a)^2 + sin(a)^2)
Степени
[src]
2
2 / I*a -I*a\
/ -I*a I*a\ |e e |
- \- e + e / + 4*|---- + -----|
\ 2 2 /
$$4 \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{2} - \left(e^{i a} - e^{- i a}\right)^{2}$$
-(-exp(-i*a) + exp(i*a))^2 + 4*(exp(i*a)/2 + exp(-i*a)/2)^2
Тригонометрическая часть
[src]
4
$$4$$
2 2/ pi\
4*sin (a) + 4*sin |a + --|
\ 2 /
$$4 \sin^{2}{\left(a \right)} + 4 \sin^{2}{\left(a + \frac{\pi}{2} \right)}$$
4 4 ------- + ------- 2 2 csc (a) sec (a)
$$\frac{4}{\sec^{2}{\left(a \right)}} + \frac{4}{\csc^{2}{\left(a \right)}}$$
2 2/ pi\
4*cos (a) + 4*cos |a - --|
\ 2 /
$$4 \cos^{2}{\left(a \right)} + 4 \cos^{2}{\left(a - \frac{\pi}{2} \right)}$$
4 4
------- + ------------
2 2/ pi\
sec (a) sec |a - --|
\ 2 /
$$\frac{4}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + \frac{4}{\sec^{2}{\left(a \right)}}$$
4 4
------- + ------------
2 2/pi \
sec (a) sec |-- - a|
\2 /
$$\frac{4}{\sec^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{4}{\sec^{2}{\left(a \right)}}$$
4 4
------- + ------------
2 2/pi \
csc (a) csc |-- - a|
\2 /
$$\frac{4}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{4}{\csc^{2}{\left(a \right)}}$$
4 4
------------ + ------------
2 2/pi \
csc (pi - a) csc |-- - a|
\2 /
$$\frac{4}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{4}{\csc^{2}{\left(- a + \pi \right)}}$$
2 10 - 8*cos(a) - 4*(1 - cos(a)) + 2*cos(2*a)
$$- 4 \left(- \cos{\left(a \right)} + 1\right)^{2} - 8 \cos{\left(a \right)} + 2 \cos{\left(2 a \right)} + 10$$
2
/ 2/a pi\\ 2
2*(1 + cos(2*a)) + |1 - cot |- + --|| *(1 + sin(a))
\ \2 4 //
$$\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\sin{\left(a \right)} + 1\right)^{2} + 2 \left(\cos{\left(2 a \right)} + 1\right)$$
2/a pi\
16*tan |- + --|
\2 4 /
2*(1 - cos(2*a)) + -------------------
2
/ 2/a pi\\
|1 + tan |- + --||
\ \2 4 //
$$2 \cdot \left(- \cos{\left(2 a \right)} + 1\right) + \frac{16 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$
2
/ 2/a\\ 2/a\
4*|1 - tan |-|| 16*tan |-|
\ \2// \2/
---------------- + --------------
2 2
/ 2/a\\ / 2/a\\
|1 + tan |-|| |1 + tan |-||
\ \2// \ \2//
$$\frac{4 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + \frac{16 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
2/a\ 2/a pi\
16*cot |-| 16*tan |- + --|
\2/ \2 4 /
-------------- + -------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + cot |-|| |1 + tan |- + --||
\ \2// \ \2 4 //
$$\frac{16 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + \frac{16 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$
2/a\ 2/a pi\
16*tan |-| 16*tan |- + --|
\2/ \2 4 /
-------------- + -------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + tan |-|| |1 + tan |- + --||
\ \2// \ \2 4 //
$$\frac{16 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{16 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
2
/ 1 \
4*|1 - -------|
| 2/a\|
| cot |-||
\ \2// 16
---------------- + ----------------------
2 2
/ 1 \ / 1 \ 2/a\
|1 + -------| |1 + -------| *cot |-|
| 2/a\| | 2/a\| \2/
| cot |-|| | cot |-||
\ \2// \ \2//
$$\frac{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} + \frac{16}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cot^{2}{\left(\frac{a}{2} \right)}}$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ || | || | 4*|< 2 | + 4*|< 2 | ||sin (a) otherwise | ||cos (a) otherwise | \\ / \\ /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right)$$
2 2
/ 2/a\\ / 2/a pi\\
4*|-1 + cot |-|| 4*|-1 + tan |- + --||
\ \2// \ \2 4 //
----------------- + ----------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + cot |-|| |1 + tan |- + --||
\ \2// \ \2 4 //
$$\frac{4 \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
2 2
/ 2/a pi\\ / 2/a\\
4*|1 - cot |- + --|| 4*|1 - tan |-||
\ \2 4 // \ \2//
--------------------- + ----------------
2 2
/ 2/a pi\\ / 2/a\\
|1 + cot |- + --|| |1 + tan |-||
\ \2 4 // \ \2//
$$\frac{4 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + \frac{4 \left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ || | || | 4*|< 2 | + 4*|< 2/ pi\ | ||sin (a) otherwise | ||sin |a + --| otherwise | \\ / \\ \ 2 / /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\sin^{2}{\left(a + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right)$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ || | || | 4*|< 2/ pi\ | + 4*|< 2 | ||cos |a - --| otherwise | ||cos (a) otherwise | \\ \ 2 / / \\ /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\cos^{2}{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right)$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ || | || | || 1 | || 1 | 4*|<------------ otherwise | + 4*|<------- otherwise | || 2/ pi\ | || 2 | ||sec |a - --| | ||sec (a) | \\ \ 2 / / \\ /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\sec^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right)\right)$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ || | || | || 1 | || 1 | 4*|<------- otherwise | + 4*|<------------ otherwise | || 2 | || 2/pi \ | ||csc (a) | ||csc |-- - a| | \\ / \\ \2 / /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\csc^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right)$$
// / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| | || \ 2 / |
4*|< 2 | + 4*|< |
||cos (a) otherwise | || 4/a\ 2/a\ |
\\ / ||- 4*cos |-| + 4*cos |-| otherwise |
\\ \2/ \2/ /
$$\left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} & \text{otherwise} \end{cases}\right)\right)$$
2
/ 4/a\\
| 4*sin |-||
| \2/|
4*|1 - ---------| 4/a\
| 2 | 64*sin |-|
\ sin (a) / \2/
------------------ + ------------------------
2 2
/ 4/a\\ / 4/a\\
| 4*sin |-|| | 4*sin |-||
| \2/| | \2/| 2
|1 + ---------| |1 + ---------| *sin (a)
| 2 | | 2 |
\ sin (a) / \ sin (a) /
$$\frac{4 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2}} + \frac{64 \sin^{4}{\left(\frac{a}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2} \sin^{2}{\left(a \right)}}$$
// / pi\ \
// 0 for a mod pi = 0\ || 0 for |a + --| mod pi = 0|
|| | || \ 2 / |
4*|< 2 | + 4*|< |
||sin (a) otherwise | || 2 2/a pi\ |
\\ / ||(1 + sin(a)) *cot |- + --| otherwise |
\\ \2 4 / /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(a \right)} + 1\right)^{2} \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right)\right)$$
// 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 | 4*|<| | + 4*|<| | ||< 2 otherwise | ||< 2 otherwise | |||sin (a) otherwise | |||cos (a) otherwise | \\\ / \\\ /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right)$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ || | || | || 2/a\ | || 2 | || 4*cot |-| | ||/ 2/a\\ | || \2/ | |||-1 + cot |-|| | 4*|<-------------- otherwise | + 4*|<\ \2// | || 2 | ||--------------- otherwise | ||/ 2/a\\ | || 2 | |||1 + cot |-|| | || / 2/a\\ | ||\ \2// | || |1 + cot |-|| | \\ / \\ \ \2// /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\ || | || | || 2/a\ | || 2 | || 4*tan |-| | ||/ 2/a\\ | || \2/ | |||1 - tan |-|| | 4*|<-------------- otherwise | + 4*|<\ \2// | || 2 | ||-------------- otherwise | ||/ 2/a\\ | || 2 | |||1 + tan |-|| | ||/ 2/a\\ | ||\ \2// | |||1 + tan |-|| | \\ / \\\ \2// /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
2
/ 2/a pi\\
| cos |- - --||
| \2 2 /|
4*|1 - ------------|
| 2/a\ | 2/a pi\
| cos |-| | 16*cos |- - --|
\ \2/ / \2 2 /
--------------------- + ---------------------------
2 2
/ 2/a pi\\ / 2/a pi\\
| cos |- - --|| | cos |- - --||
| \2 2 /| | \2 2 /| 2/a\
|1 + ------------| |1 + ------------| *cos |-|
| 2/a\ | | 2/a\ | \2/
| cos |-| | | cos |-| |
\ \2/ / \ \2/ /
$$\frac{4 \left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} + \frac{16 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cos^{2}{\left(\frac{a}{2} \right)}}$$
2
/ 2/a\ \
| sec |-| |
| \2/ |
4*|1 - ------------|
| 2/a pi\| 2/a\
| sec |- - --|| 16*sec |-|
\ \2 2 // \2/
--------------------- + --------------------------------
2 2
/ 2/a\ \ / 2/a\ \
| sec |-| | | sec |-| |
| \2/ | | \2/ | 2/a pi\
|1 + ------------| |1 + ------------| *sec |- - --|
| 2/a pi\| | 2/a pi\| \2 2 /
| sec |- - --|| | sec |- - --||
\ \2 2 // \ \2 2 //
$$\frac{4 \left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}} + \frac{16 \sec^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
2
/ 2/pi a\\
| csc |-- - -||
| \2 2/|
4*|1 - ------------|
| 2/a\ | 2/pi a\
| csc |-| | 16*csc |-- - -|
\ \2/ / \2 2/
--------------------- + ---------------------------
2 2
/ 2/pi a\\ / 2/pi a\\
| csc |-- - -|| | csc |-- - -||
| \2 2/| | \2 2/| 2/a\
|1 + ------------| |1 + ------------| *csc |-|
| 2/a\ | | 2/a\ | \2/
| csc |-| | | csc |-| |
\ \2/ / \ \2/ /
$$\frac{4 \left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} + \frac{16 \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \csc^{2}{\left(\frac{a}{2} \right)}}$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 1 \ |
|| 4 | |||-1 + -------| |
||---------------------- otherwise | ||| 2/a\| |
|| 2 | ||| tan |-|| |
4*|
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \tan^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
// / pi\ \
// 0 for a mod pi = 0\ || 0 for |a + --| mod pi = 0|
|| | || \ 2 / |
|| 2/a\ | || |
|| 4*cot |-| | || 2/a pi\ |
|| \2/ | || 4*cot |- + --| |
4*|<-------------- otherwise | + 4*|< \2 4 / |
|| 2 | ||------------------- otherwise |
||/ 2/a\\ | || 2 |
|||1 + cot |-|| | ||/ 2/a pi\\ |
||\ \2// | |||1 + cot |- + --|| |
\\ / ||\ \2 4 // |
\\ /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
// / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| | || \ 2 / |
|| 2 | || |
||/ 2/a\\ | || 2 |
|||-1 + cot |-|| | ||/ 2/a pi\\ |
4*|<\ \2// | + 4*|<|-1 + tan |- + --|| |
||--------------- otherwise | ||\ \2 4 // |
|| 2 | ||-------------------- otherwise |
|| / 2/a\\ | || 2 |
|| |1 + cot |-|| | ||/ 2/a pi\\ |
\\ \ \2// / |||1 + tan |- + --|| |
\\\ \2 4 // /
$$\left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
// 0 for a mod pi = 0\
|| | // 1 for a mod 2*pi = 0\
|| 2 | || |
|| sin (a) | || 2 |
||------------------------ otherwise | ||/ 2 4/a\\ |
|| 2 | |||sin (a) - 4*sin |-|| |
4*|
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin^{2}{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(- 4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}}{\left(4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 2 \ |
|| 2 | ||| sin (a) | |
|| sin (a) | |||-1 + ---------| |
||------------------------ otherwise | ||| 4/a\| |
|| 2 | ||| 4*sin |-|| |
4*|
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin^{2}{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
// 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 | ||| | ||| | ||| 2/a\ | ||| 2 | ||| 4*cot |-| | |||/ 2/a\\ | 4*|<| \2/ | + 4*|<||-1 + cot |-|| | ||<-------------- otherwise otherwise | ||<\ \2// otherwise | ||| 2 | |||--------------- otherwise | |||/ 2/a\\ | ||| 2 | ||||1 + cot |-|| | ||| / 2/a\\ | |||\ \2// | ||| |1 + cot |-|| | \\\ / \\\ \ \2// /
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right)$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 2/a\ \ |
|| 2/a\ | ||| cos |-| | |
|| 4*cos |-| | ||| \2/ | |
|| \2/ | |||-1 + ------------| |
||-------------------------------- otherwise | ||| 2/a pi\| |
|| 2 | ||| cos |- - --|| |
4*|
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cos^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 2/a pi\\ |
|| 2/a pi\ | ||| sec |- - --|| |
|| 4*sec |- - --| | ||| \2 2 /| |
|| \2 2 / | |||-1 + ------------| |
||--------------------------- otherwise | ||| 2/a\ | |
|| 2 | ||| sec |-| | |
4*|
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \sec^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 2/a\ \ |
|| 2/a\ | ||| csc |-| | |
|| 4*csc |-| | ||| \2/ | |
|| \2/ | |||-1 + ------------| |
||-------------------------------- otherwise | ||| 2/pi a\| |
|| 2 | ||| csc |-- - -|| |
4*|
$$\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \csc^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2} \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right)$$
4*Piecewise((0, Mod(a = pi, 0)), (4*csc(a/2)^2/((1 + csc(a/2)^2/csc(pi/2 - a/2)^2)^2*csc(pi/2 - a/2)^2), True)) + 4*Piecewise((1, Mod(a = 2*pi, 0)), ((-1 + csc(a/2)^2/csc(pi/2 - a/2)^2)^2/(1 + csc(a/2)^2/csc(pi/2 - a/2)^2)^2, True))