Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- 1+sin(pi/2-a)*cos(pi-a)*sin(a)^2 если a=-1/3
- 25*cos(x)^2*sin(y)^2+25*cos(x)^2*cos(y)^2 если y=1
- sin(4*pi+x) если x=-1
- 12*x*3*y*5*z если y=3/2
- Разложить многочлен на множители:
- 27-x^9
- 64-27*a^3
- m^8-6*m^4*n^5+9*n^10
- x^6+1
- Общий знаменатель:
- (x-9)/x^2-18*x+81/x+9
- (12-a^2/a+3+a-3)/(1/a+3+a/a^2-9+5/3-a)
- (sin(a+pi/12)+sin(a-pi/2))*sin(pi)/12
- 5*b/b-3-b+6/2*b-6*90/b^2+6*b
- Умножение столбиком:
- 18*31
- 1250*80
- 68*17
- 70*20
- Деление столбиком:
- 756/6
- 5000/7
- 89/9
- 241/4
- Раскрыть скобки в:
- 8*(6*a-7)-17*a
- (x-3)*(x-4)-(x+4)^2
- 2*(x+1)^2
- (8*a+b)*(b-8*a)
- Разложение числа на простые множители:
- 8505
- 15552
- 10327
- 208
- Производная:
- -1/3
- Интеграл d{x}:
-
-1/3
-
Идентичные выражения
- один +sin(pi/ два -a)*cos(pi-a)*sin(a)^ два если a=- один / три
- 1 плюс синус от ( число пи делить на 2 минус a) умножить на косинус от ( число пи минус a) умножить на синус от (a) в квадрате если a равно минус 1 делить на 3
- один плюс синус от ( число пи делить на два минус a) умножить на косинус от ( число пи минус a) умножить на синус от (a) в степени два если a равно минус один делить на три
- 1+sin(pi/2-a)*cos(pi-a)*sin(a)2 если a=-1/3
- 1+sinpi/2-a*cospi-a*sina2 если a=-1/3
- 1+sin(pi/2-a)*cos(pi-a)*sin(a)² если a=-1/3
- 1+sin(pi/2-a)*cos(pi-a)*sin(a) в степени 2 если a=-1/3
- 1+sin(pi/2-a)cos(pi-a)sin(a)^2 если a=-1/3
- 1+sin(pi/2-a)cos(pi-a)sin(a)2 если a=-1/3
- 1+sinpi/2-acospi-asina2 если a=-1/3
- 1+sinpi/2-acospi-asina^2 если a=-1/3
- 1+sin(pi/2-a)*cos(pi-a)*sin(a)^2 при a=-1/3
- 1+sin(pi разделить на 2-a)*cos(pi-a)*sin(a)^2 если a=-1 разделить на 3
-
Похожие выражения
- 1+sin(pi/2-a)*cos(pi-a)*sin(a)^2 если a=+1/3
- 1+sin(pi/2+a)*cos(pi-a)*sin(a)^2 если a=-1/3
- 1-sin(pi/2-a)*cos(pi-a)*sin(a)^2 если a=-1/3
- 1+sin(pi/2-a)*cos(pi+a)*sin(a)^2 если a=-1/3
-
Что Вы имели ввиду?
- 1 + sin(pi/(2 - a))*cos(pi - a)*sin(a)^2
- 1 + sin(pi/2 - a)*cos(pi - a)*sin(a)^2
- 1 + sin(pi/2 - a)*cos(pi - a)*sin(a)^2
1+sin(pi/2-a)*cos(pi-a)*sin(a)^2 если a=-1/3
Решение
Вы ввели
[src]
/pi \ 2
1 + sin|-- - a|*cos(pi - a)*sin (a)
\2 /
$$\sin^{2}{\left(a \right)} \sin{\left(- a + \frac{\pi}{2} \right)} \cos{\left(- a + \pi \right)} + 1$$
1 + sin(pi/2 - a)*cos(pi - a)*sin(a)^2
Общее упрощение
[src]
7 cos(4*a) - + -------- 8 8
$$\frac{\cos{\left(4 a \right)}}{8} + \frac{7}{8}$$
7/8 + cos(4*a)/8
Подстановка условия
[src]
1 + sin(pi/2 - a)*cos(pi - a)*sin(a)^2 при a = -1/3
подставляем
/pi \ 2
1 + sin|-- - a|*cos(pi - a)*sin (a)
\2 /
$$\sin^{2}{\left(a \right)} \sin{\left(- a + \frac{\pi}{2} \right)} \cos{\left(- a + \pi \right)} + 1$$
7 cos(4*a) - + -------- 8 8
$$\frac{\cos{\left(4 a \right)}}{8} + \frac{7}{8}$$
переменные
a = -1/3
$$a = - \frac{1}{3}$$
7 cos(4*(-1/3)) - + ------------- 8 8
$$\frac{\cos{\left(4 (-1/3) \right)}}{8} + \frac{7}{8}$$
7 cos(4/3) - + -------- 8 8
$$\frac{\cos{\left(\frac{4}{3} \right)}}{8} + \frac{7}{8}$$
7/8 + cos(4/3)/8
Собрать выражение
[src]
7 cos(4*a) - + -------- 8 8
$$\frac{\cos{\left(4 a \right)}}{8} + \frac{7}{8}$$
7/8 + cos(4*a)/8
Степени
[src]
2 2 1 - cos (a)*sin (a)
$$- \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} + 1$$
2 1 + sin (a)*cos(a)*cos(pi - a)
$$\sin^{2}{\left(a \right)} \cos{\left(a \right)} \cos{\left(- a + \pi \right)} + 1$$
/ / pi\ /pi \\
2 / I*(pi - a) I*(a - pi)\ | I*|a - --| I*|-- - a||
/ -I*a I*a\ |e e | | \ 2 / \2 /|
I*\- e + e / *|----------- + -----------|*\- e + e /
\ 2 2 /
1 + -----------------------------------------------------------------------------
8
$$\frac{i \left(e^{i a} - e^{- i a}\right)^{2} \left(\frac{e^{i \left(- a + \pi\right)}}{2} + \frac{e^{i \left(a - \pi\right)}}{2}\right) \left(e^{i \left(- a + \frac{\pi}{2}\right)} - e^{i \left(a - \frac{\pi}{2}\right)}\right)}{8} + 1$$
1 + i*(-exp(-i*a) + exp(i*a))^2*(exp(i*(pi - a))/2 + exp(i*(a - pi))/2)*(-exp(i*(a - pi/2)) + exp(i*(pi/2 - a)))/8
Общий знаменатель
[src]
2 2 1 - cos (a)*sin (a)
$$- \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} + 1$$
1 - cos(a)^2*sin(a)^2
Рациональный знаменатель
[src]
2 2 1 - cos (a)*sin (a)
$$- \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} + 1$$
1 - cos(a)^2*sin(a)^2
Комбинаторика
[src]
-(1 + cos(a)*sin(a))*(-1 + cos(a)*sin(a))
$$- \left(\sin{\left(a \right)} \cos{\left(a \right)} - 1\right) \left(\sin{\left(a \right)} \cos{\left(a \right)} + 1\right)$$
-(1 + cos(a)*sin(a))*(-1 + cos(a)*sin(a))
Тригонометрическая часть
[src]
2
sin (2*a)
1 - ---------
4
$$- \frac{\sin^{2}{\left(2 a \right)}}{4} + 1$$
1 - cos(4*a)
1 - ------------
8
$$- \frac{- \cos{\left(4 a \right)} + 1}{8} + 1$$
7 cos(4*a) - + -------- 8 8
$$\frac{\cos{\left(4 a \right)}}{8} + \frac{7}{8}$$
7 1 - + ---------- 8 8*sec(4*a)
$$\frac{7}{8} + \frac{1}{8 \sec{\left(4 a \right)}}$$
4 2 1 + sin (a) - sin (a)
$$\sin^{4}{\left(a \right)} - \sin^{2}{\left(a \right)} + 1$$
2 2 1 - cos (a)*sin (a)
$$- \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} + 1$$
/pi \
sin|-- + 4*a|
7 \2 /
- + -------------
8 8
$$\frac{\sin{\left(4 a + \frac{\pi}{2} \right)}}{8} + \frac{7}{8}$$
1
1 - ---------------
2 2
csc (a)*sec (a)
$$1 - \frac{1}{\csc^{2}{\left(a \right)} \sec^{2}{\left(a \right)}}$$
7 1
- + ---------------
8 /pi \
8*csc|-- - 4*a|
\2 /
$$\frac{7}{8} + \frac{1}{8 \csc{\left(- 4 a + \frac{\pi}{2} \right)}}$$
2 2/ pi\
1 - cos (a)*cos |a - --|
\ 2 /
$$- \cos^{2}{\left(a \right)} \cos^{2}{\left(a - \frac{\pi}{2} \right)} + 1$$
2 2/ pi\
1 - sin (a)*sin |a + --|
\ 2 /
$$- \sin^{2}{\left(a \right)} \sin^{2}{\left(a + \frac{\pi}{2} \right)} + 1$$
1
1 - --------------------
2 2/ pi\
sec (a)*sec |a - --|
\ 2 /
$$1 - \frac{1}{\sec^{2}{\left(a \right)} \sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$
1
1 - --------------------
2 2/pi \
csc (a)*csc |-- - a|
\2 /
$$1 - \frac{1}{\csc^{2}{\left(a \right)} \csc^{2}{\left(- a + \frac{\pi}{2} \right)}}$$
1
1 - --------------------
2 2/pi \
sec (a)*sec |-- - a|
\2 /
$$1 - \frac{1}{\sec^{2}{\left(a \right)} \sec^{2}{\left(- a + \frac{\pi}{2} \right)}}$$
1
1 - -------------------------
2 2/pi \
csc (pi - a)*csc |-- - a|
\2 /
$$1 - \frac{1}{\csc^{2}{\left(- a + \pi \right)} \csc^{2}{\left(- a + \frac{\pi}{2} \right)}}$$
2
7 1 - tan (2*a)
- + -----------------
8 / 2 \
8*\1 + tan (2*a)/
$$\frac{- \tan^{2}{\left(2 a \right)} + 1}{8 \left(\tan^{2}{\left(2 a \right)} + 1\right)} + \frac{7}{8}$$
/1 cos(2*a)\ /1 cos(2*a)\
1 - |- + --------|*|- - --------|
\2 2 / \2 2 /
$$- \left(- \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2}\right) \left(\frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2}\right) + 1$$
2
/ 2/a\\ 8/a\ 2/a\
1 - 4*|1 - tan |-|| *cos |-|*tan |-|
\ \2// \2/ \2/
$$- 4 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cos^{8}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{a}{2} \right)} + 1$$
2
/ 2/a\\ 6/a\ 2/a\
1 - 4*|1 - tan |-|| *cos |-|*sin |-|
\ \2// \2/ \2/
$$- 4 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \sin^{2}{\left(\frac{a}{2} \right)} \cos^{6}{\left(\frac{a}{2} \right)} + 1$$
2
/ 2/a\\ 2/a\
4*|1 - tan |-|| *tan |-|
\ \2// \2/
1 - ------------------------
4
/ 2/a\\
|1 + tan |-||
\ \2//
$$- \frac{4 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{4}} + 1$$
2
/ 1 \
4*|1 - -------|
| 2/a\|
| cot |-||
\ \2//
1 - ----------------------
4
/ 1 \ 2/a\
|1 + -------| *cot |-|
| 2/a\| \2/
| cot |-||
\ \2//
$$1 - \frac{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{4} \cot^{2}{\left(\frac{a}{2} \right)}}$$
2 2
/ /a\\ / /a\\ 6/a\ 2/a\
1 - 4*|1 + tan|-|| *|-1 + tan|-|| *cos |-|*sin |-|
\ \2// \ \2// \2/ \2/
$$- 4 \left(\tan{\left(\frac{a}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{2} \sin^{2}{\left(\frac{a}{2} \right)} \cos^{6}{\left(\frac{a}{2} \right)} + 1$$
/ 1 for 2*a mod pi = 0
|
| 2
<-1 + cot (2*a)
|-------------- otherwise
| 2
7 \1 + cot (2*a)
- + -----------------------------------
8 8
$$\left(\frac{\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(2 a \right)} - 1}{\cot^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}}{8}\right) + \frac{7}{8}$$
/ 1 for 2*a mod pi = 0
|
< 2 / 2 \
|sin (2*a)*\-1 + cot (2*a)/ otherwise
7 \
- + -----------------------------------------------
8 8
$$\left(\frac{\begin{cases} 1 & \text{for}\: 2 a \bmod \pi = 0 \\\left(\cot^{2}{\left(2 a \right)} - 1\right) \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}}{8}\right) + \frac{7}{8}$$
2 8
/ 2/a\\ / 2/a\\ 16/a\ 2/a\
1 - 4*|1 - tan |-|| *|1 - tan |-|| *cos |-|*tan |-|
\ \2// \ \4// \4/ \2/
$$- 4 \left(- \tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{8} \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cos^{16}{\left(\frac{a}{4} \right)} \tan^{2}{\left(\frac{a}{2} \right)} + 1$$
2 2
/ /a\\ / /a\\ 4/a\
|1 + tan|-|| *|-1 + tan|-|| *cos |-|*(1 - cos(2*a))
\ \2// \ \2// \2/
1 - ---------------------------------------------------
2
$$- \frac{\left(- \cos{\left(2 a \right)} + 1\right) \left(\tan{\left(\frac{a}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{2} \cos^{4}{\left(\frac{a}{2} \right)}}{2} + 1$$
/ 2 2 \ / 2 2 \
|1 cos (a) sin (a)| |1 sin (a) cos (a)|
1 - |- + ------- - -------|*|- + ------- - -------|
\2 2 2 / \2 2 2 /
$$- \left(- \frac{\sin^{2}{\left(a \right)}}{2} + \frac{\cos^{2}{\left(a \right)}}{2} + \frac{1}{2}\right) \left(\frac{\sin^{2}{\left(a \right)}}{2} - \frac{\cos^{2}{\left(a \right)}}{2} + \frac{1}{2}\right) + 1$$
2
/ 2/a pi\\
| cos |- - --||
| \2 2 /| 6/a\ 2/a pi\
1 - 4*|1 - ------------| *cos |-|*cos |- - --|
| 2/a\ | \2/ \2 2 /
| cos |-| |
\ \2/ /
$$- 4 \left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cos^{6}{\left(\frac{a}{2} \right)} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} + 1$$
2
/ 2/a\ \
| sec |-| |
| \2/ |
4*|1 - ------------|
| 2/a pi\|
| sec |- - --||
\ \2 2 //
1 - ---------------------
6/a\ 2/a pi\
sec |-|*sec |- - --|
\2/ \2 2 /
$$1 - \frac{4 \left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\sec^{6}{\left(\frac{a}{2} \right)} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
2
/ 2/pi a\\
| csc |-- - -||
| \2 2/|
4*|1 - ------------|
| 2/a\ |
| csc |-| |
\ \2/ /
1 - ---------------------
2/a\ 6/pi a\
csc |-|*csc |-- - -|
\2/ \2 2/
$$1 - \frac{4 \left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\csc^{2}{\left(\frac{a}{2} \right)} \csc^{6}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}$$
2
/ 4/a\\
| 4*sin |-||
| \2/| 4/a\ 8/pi a\
16*|1 - ---------| *sin |-|*sin |-- + -|
| 2 | \2/ \2 2/
\ sin (a) /
1 - ----------------------------------------
2
sin (a)
$$- \frac{16 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)} \sin^{8}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1$$
2 8
/ 2/a\\ / 2/a\\ 2/a\
4*|1 - tan |-|| *|1 - tan |-|| *tan |-|
\ \2// \ \4// \2/
1 - ---------------------------------------
8
/ 2/a\\
|1 + tan |-||
\ \4//
$$- \frac{4 \left(- \tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{8} \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{8}} + 1$$
8 16/a\ 4 8/a\
sin (a) + 256*sin |-| + 224*sin (a)*sin |-|
\2/ \2/
--------------------------------------------
4
/ 2 4/a\\
|sin (a) + 4*sin |-||
\ \2//
$$\frac{256 \sin^{16}{\left(\frac{a}{2} \right)} + 224 \sin^{8}{\left(\frac{a}{2} \right)} \sin^{4}{\left(a \right)} + \sin^{8}{\left(a \right)}}{\left(4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{4}}$$
2 2
/ 2/a pi\\ / 2/a\\ 2 4/a\
|1 - cot |- + --|| *|1 - tan |-|| *(1 + sin(a)) *cos |-|
\ \2 4 // \ \2// \2/
1 - --------------------------------------------------------
4
$$- \frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\sin{\left(a \right)} + 1\right)^{2} \cos^{4}{\left(\frac{a}{2} \right)}}{4} + 1$$
2/a\ 2/a pi\
16*cot |-|*tan |- + --|
\2/ \2 4 /
1 - ----------------------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + cot |-|| *|1 + tan |- + --||
\ \2// \ \2 4 //
$$1 - \frac{16 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
2/a\ 2/a pi\
16*tan |-|*tan |- + --|
\2/ \2 4 /
1 - ----------------------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + tan |-|| *|1 + tan |- + --||
\ \2// \ \2 4 //
$$1 - \frac{16 \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$
2 2
/ 2/a\\ / 2/a pi\\ 4/a\
|-1 + cot |-|| *|-1 + tan |- + --|| *sin |-|
\ \2// \ \2 4 // \2/
1 - --------------------------------------------
2
/ 2/a pi\\
|1 + tan |- + --||
\ \2 4 //
$$- \frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
1 - |< 2 |*|< 2 |
||sin (a) otherwise | ||cos (a) otherwise |
\\ / \\ /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + 1$$
2
/ 4/a\\
| 4*sin |-||
| \2/| 4/a\
16*|1 - ---------| *sin |-|
| 2 | \2/
\ sin (a) /
1 - ---------------------------
4
/ 4/a\\
| 4*sin |-||
| \2/| 2
|1 + ---------| *sin (a)
| 2 |
\ sin (a) /
$$- \frac{16 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{4} \sin^{2}{\left(a \right)}} + 1$$
2 2
/ 2/a\\ / 2/a pi\\
|-1 + cot |-|| *|-1 + tan |- + --||
\ \2// \ \2 4 //
1 - ------------------------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + cot |-|| *|1 + tan |- + --||
\ \2// \ \2 4 //
$$- \frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
1 - |< 2 |*|< 2/ pi\ |
||sin (a) otherwise | ||sin |a + --| otherwise |
\\ / \\ \ 2 / /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\sin^{2}{\left(a + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
1 - |< 2/ pi\ |*|< 2 |
||cos |a - --| otherwise | ||cos (a) otherwise |
\\ \ 2 / / \\ /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\cos^{2}{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + 1$$
2 2
/ 2/a pi\\ / 2/a\\
|1 - cot |- + --|| *|1 - tan |-||
\ \2 4 // \ \2//
1 - ----------------------------------
2 2
/ 2/a pi\\ / 2/a\\
|1 + cot |- + --|| *|1 + tan |-||
\ \2 4 // \ \2//
$$- \frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| 1 | || 1 |
1 - |<------------ otherwise |*|<------- otherwise |
|| 2/ pi\ | || 2 |
||sec |a - --| | ||sec (a) |
\\ \ 2 / / \\ /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\sec^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| 1 | || 1 |
1 - |<------- otherwise |*|<------------ otherwise |
|| 2 | || 2/pi \ |
||csc (a) | ||csc |-- - a| |
\\ / \\ \2 / /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\csc^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// a \
|| 1 for - mod 2*pi = 0|
2 || 2 |
/ 2/a\\ 2/a\ || |
1 - 4*|1 - tan |-|| *tan |-|*|< 8 |
\ \2// \2/ ||/ 2/a\\ 16/a\ |
|||-1 + cot |-|| *sin |-| otherwise |
||\ \4// \4/ |
\\ /
$$\left(- 4 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\begin{cases} 1 & \text{for}\: \frac{a}{2} \bmod 2 \pi = 0 \\\left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{8} \sin^{16}{\left(\frac{a}{4} \right)} & \text{otherwise} \end{cases}\right) \tan^{2}{\left(\frac{a}{2} \right)}\right) + 1$$
2
/ 2/a pi\\
| cos |- - --||
| \2 2 /| 2/a pi\
4*|1 - ------------| *cos |- - --|
| 2/a\ | \2 2 /
| cos |-| |
\ \2/ /
1 - ----------------------------------
4
/ 2/a pi\\
| cos |- - --||
| \2 2 /| 2/a\
|1 + ------------| *cos |-|
| 2/a\ | \2/
| cos |-| |
\ \2/ /
$$1 - \frac{4 \left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{4} \cos^{2}{\left(\frac{a}{2} \right)}}$$
2
/ 2/a\ \
| sec |-| |
| \2/ | 2/a\
4*|1 - ------------| *sec |-|
| 2/a pi\| \2/
| sec |- - --||
\ \2 2 //
1 - --------------------------------
4
/ 2/a\ \
| sec |-| |
| \2/ | 2/a pi\
|1 + ------------| *sec |- - --|
| 2/a pi\| \2 2 /
| sec |- - --||
\ \2 2 //
$$1 - \frac{4 \left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \sec^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{4} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
2
/ 2/pi a\\
| csc |-- - -||
| \2 2/| 2/pi a\
4*|1 - ------------| *csc |-- - -|
| 2/a\ | \2 2/
| csc |-| |
\ \2/ /
1 - ----------------------------------
4
/ 2/pi a\\
| csc |-- - -||
| \2 2/| 2/a\
|1 + ------------| *csc |-|
| 2/a\ | \2/
| csc |-| |
\ \2/ /
$$1 - \frac{4 \left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{4} \csc^{2}{\left(\frac{a}{2} \right)}}$$
// / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| | || \ 2 / |
1 - |< 2 |*|< |
||cos (a) otherwise | || 4/a\ 2/a\ |
\\ / ||- 4*cos |-| + 4*cos |-| otherwise |
\\ \2/ \2/ /
$$\left(- \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + 1$$
// / pi\ \
// 0 for a mod pi = 0\ || 0 for |a + --| mod pi = 0|
|| | || \ 2 / |
1 - |< 2 |*|< |
||sin (a) otherwise | || 2 2/a pi\ |
\\ / ||(1 + sin(a)) *cot |- + --| otherwise |
\\ \2 4 / /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(a \right)} + 1\right)^{2} \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right)\right) + 1$$
// a \
|| 1 for - mod 2*pi = 0|
|| 2 |
|| |
2 || 8 |
/ 1 \ ||/ 2/a\\ |
4*|1 - -------| *|<|-1 + cot |-|| |
| 2/a\| ||\ \4// |
| cot |-|| ||--------------- otherwise |
\ \2// || 8 |
|| / 2/a\\ |
|| |1 + cot |-|| |
\\ \ \4// /
1 - -------------------------------------------------------
2/a\
cot |-|
\2/
$$\left(- \frac{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \left(\begin{cases} 1 & \text{for}\: \frac{a}{2} \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{8}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{8}} & \text{otherwise} \end{cases}\right)}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) + 1$$
// 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 |
1 - |<| |*|<| |
||< 2 otherwise | ||< 2 otherwise |
|||sin (a) otherwise | |||cos (a) otherwise |
\\\ / \\\ /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| 2/a\ | || 2 |
|| 4*cot |-| | ||/ 2/a\\ |
|| \2/ | |||-1 + cot |-|| |
1 - |<-------------- otherwise |*|<\ \2// |
|| 2 | ||--------------- otherwise |
||/ 2/a\\ | || 2 |
|||1 + cot |-|| | || / 2/a\\ |
||\ \2// | || |1 + cot |-|| |
\\ / \\ \ \2// /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| 2/a\ | || 2 |
|| 4*tan |-| | ||/ 2/a\\ |
|| \2/ | |||1 - tan |-|| |
1 - |<-------------- otherwise |*|<\ \2// |
|| 2 | ||-------------- otherwise |
||/ 2/a\\ | || 2 |
|||1 + tan |-|| | ||/ 2/a\\ |
||\ \2// | |||1 + tan |-|| |
\\ / \\\ \2// /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 1 \ |
|| 4 | |||-1 + -------| |
||---------------------- otherwise | ||| 2/a\| |
|| 2 | ||| tan |-|| |
1 - |
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \tan^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// / pi\ \
// 0 for a mod pi = 0\ || 0 for |a + --| mod pi = 0|
|| | || \ 2 / |
|| 2/a\ | || |
|| 4*cot |-| | || 2/a pi\ |
|| \2/ | || 4*cot |- + --| |
1 - |<-------------- otherwise |*|< \2 4 / |
|| 2 | ||------------------- otherwise |
||/ 2/a\\ | || 2 |
|||1 + cot |-|| | ||/ 2/a pi\\ |
||\ \2// | |||1 + cot |- + --|| |
\\ / ||\ \2 4 // |
\\ /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// / 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\\ |
1 - |<\ \2// |*|<|-1 + tan |- + --|| |
||--------------- otherwise | ||\ \2 4 // |
|| 2 | ||-------------------- otherwise |
|| / 2/a\\ | || 2 |
|| |1 + cot |-|| | ||/ 2/a pi\\ |
\\ \ \2// / |||1 + tan |- + --|| |
\\\ \2 4 // /
$$\left(- \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 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 |-|| |
1 - |
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin^{2}{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(- 4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}}{\left(4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 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 |-|| |
1 - |
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin^{2}{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 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 |
||| | ||| |
||| 2/a\ | ||| 2 |
||| 4*cot |-| | |||/ 2/a\\ |
1 - |<| \2/ |*|<||-1 + cot |-|| |
||<-------------- otherwise otherwise | ||<\ \2// otherwise |
||| 2 | |||--------------- otherwise |
|||/ 2/a\\ | ||| 2 |
||||1 + cot |-|| | ||| / 2/a\\ |
|||\ \2// | ||| |1 + cot |-|| |
\\\ / \\\ \ \2// /
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 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 |- - --|| |
1 - |
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cos^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 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 |-| | |
1 - |
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \sec^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// 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 |-- - -|| |
1 - |
$$\left(- \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \csc^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2} \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
1 - 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))*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))
Численный ответ
[src]
1.0 + sin(a)^2*cos(pi - a)*sin(pi/2 - a)
1.0 + sin(a)^2*cos(pi - a)*sin(pi/2 - a)
Объединение рациональных выражений
[src]
2 /pi - 2*a\
1 - sin (a)*cos(a)*sin|--------|
\ 2 /
$$- \sin^{2}{\left(a \right)} \sin{\left(\frac{- 2 a + \pi}{2} \right)} \cos{\left(a \right)} + 1$$
1 - sin(a)^2*cos(a)*sin((pi - 2*a)/2)