Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- sin(270-a)-cos(180+a) если a=-3
- sqrt(x-2*sqrt(x-1))+sqrt(x+2*sqrt(x-1)) если x=-3
- cot(a)^2*(cos(a)^2-1)+1 если a=1/3
- (x^(-2))^((-4*x)^(-7)) если x=2
- Разложить многочлен на множители:
- c^2-8*c+16
- x^2-26*x+169
- 400-m^2
- x^3-27
- Общий знаменатель:
- 2*cos(-2*pi-b)+sin(-pi/2+b)/2*cos(b+pi)
- pi/2-pi/4
- a^-1+6/a^-2-10*a^-1+25/a^-2-36/5*a^-1-25-5/a^-1-6
- 2+sqrt(3)/sqrt(2)+sqrt(2+sqrt(3))/2-sqrt(3)/sqrt(2)-sqrt(2-sqrt(3))
- Умножение столбиком:
- 90*15
- 70*13
- 45*32
- 72*12
- Деление столбиком:
- 681/3
- 478/4
- 5910/3
- 276/8
- Раскрыть скобки в:
- 7*b*(2*b+3)-(b+6)*(b-5)
- (a+5)*(a-3)
- (a^(-5))^2*a^12
- (m+3*n)*(m-3*n)
- Разложение числа на простые множители:
- 388
- 4860
- 6652
- 23716
- Производная:
- 1/3
- График функции y =:
- 1/3
- Интеграл d{x}:
-
1/3
-
Идентичные выражения
- cot(a)^ два *(cos(a)^ два - один)+ один если a= один / три
- котангенс от (a) в квадрате умножить на ( косинус от (a) в квадрате минус 1) плюс 1 если a равно 1 делить на 3
- котангенс от (a) в степени два умножить на ( косинус от (a) в степени два минус один) плюс один если a равно один делить на три
- cot(a)2*(cos(a)2-1)+1 если a=1/3
- cota2*cosa2-1+1 если a=1/3
- cot(a)²*(cos(a)²-1)+1 если a=1/3
- cot(a) в степени 2*(cos(a) в степени 2-1)+1 если a=1/3
- cot(a)^2(cos(a)^2-1)+1 если a=1/3
- cot(a)2(cos(a)2-1)+1 если a=1/3
- cota2cosa2-1+1 если a=1/3
- cota^2cosa^2-1+1 если a=1/3
- cot(a)^2*(cos(a)^2-1)+1 при a=1/3
- cot(a)^2*(cos(a)^2-1)+1 если a=1 разделить на 3
-
Похожие выражения
- cot(a)^2*(cos(a)^2-1)-1 если a=1/3
- cot(a)^2*(cos(a)^2+1)+1 если a=1/3
cot(a)^2*(cos(a)^2-1)+1 если a=1/3
Решение
Вы ввели
[src]
2 / 2 \ cot (a)*\cos (a) - 1/ + 1
$$\left(\cos^{2}{\left(a \right)} - 1\right) \cot^{2}{\left(a \right)} + 1$$
cot(a)^2*(cos(a)^2 - 1*1) + 1
Подстановка условия
[src]
cot(a)^2*(cos(a)^2 - 1*1) + 1 при a = 1/3
подставляем
2 / 2 \ cot (a)*\cos (a) - 1/ + 1
$$\left(\cos^{2}{\left(a \right)} - 1\right) \cot^{2}{\left(a \right)} + 1$$
2 sin (a)
$$\sin^{2}{\left(a \right)}$$
переменные
a = 1/3
$$a = \frac{1}{3}$$
2 sin ((1/3))
$$\sin^{2}{\left((1/3) \right)}$$
2 sin (1/3)
$$\sin^{2}{\left(\frac{1}{3} \right)}$$
sin(1/3)^2
Рациональный знаменатель
[src]
2 2 2 1 - cot (a) + cos (a)*cot (a)
$$\cos^{2}{\left(a \right)} \cot^{2}{\left(a \right)} - \cot^{2}{\left(a \right)} + 1$$
1 - cot(a)^2 + cos(a)^2*cot(a)^2
Комбинаторика
[src]
2 2 2 1 - cot (a) + cos (a)*cot (a)
$$\cos^{2}{\left(a \right)} \cot^{2}{\left(a \right)} - \cot^{2}{\left(a \right)} + 1$$
1 - cot(a)^2 + cos(a)^2*cot(a)^2
Степени
[src]
/ 2\
| / I*a -I*a\ |
2 | |e e | |
1 + cot (a)*|-1 + |---- + -----| |
\ \ 2 2 / /
$$\left(\left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{2} - 1\right) \cot^{2}{\left(a \right)} + 1$$
1 + cot(a)^2*(-1 + (exp(i*a)/2 + exp(-i*a)/2)^2)
Общий знаменатель
[src]
2 2 2 1 - cot (a) + cos (a)*cot (a)
$$\cos^{2}{\left(a \right)} \cot^{2}{\left(a \right)} - \cot^{2}{\left(a \right)} + 1$$
1 - cot(a)^2 + cos(a)^2*cot(a)^2
Собрать выражение
[src]
2 / 1 cos(2*a)\
1 + cot (a)*|- - + --------|
\ 2 2 /
$$\left(\frac{\cos{\left(2 a \right)}}{2} - \frac{1}{2}\right) \cot^{2}{\left(a \right)} + 1$$
1 + cot(a)^2*(-1/2 + cos(2*a)/2)
Тригонометрическая часть
[src]
2 sin (a)
$$\sin^{2}{\left(a \right)}$$
1 ------- 2 csc (a)
$$\frac{1}{\csc^{2}{\left(a \right)}}$$
2/ pi\
cos |a - --|
\ 2 /
$$\cos^{2}{\left(a - \frac{\pi}{2} \right)}$$
1 cos(2*a) - - -------- 2 2
$$- \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2}$$
1
------------
2/ pi\
sec |a - --|
\ 2 /
$$\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$
2 / 1 cos(2*a)\
1 + cot (a)*|- - + --------|
\ 2 2 /
$$\left(\frac{\cos{\left(2 a \right)}}{2} - \frac{1}{2}\right) \cot^{2}{\left(a \right)} + 1$$
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 \
$$\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}$$
2 / 2 \
cos (a)*\-1 + cos (a)/
1 + ----------------------
2
sin (a)
$$\frac{\left(\cos^{2}{\left(a \right)} - 1\right) \cos^{2}{\left(a \right)}}{\sin^{2}{\left(a \right)}} + 1$$
2 / 2 \
sin (2*a)*\-1 + cos (a)/
1 + ------------------------
4
4*sin (a)
$$1 + \frac{\left(\cos^{2}{\left(a \right)} - 1\right) \sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}$$
2 / 1 \
csc (a)*|-1 + -------|
| 2 |
\ sec (a)/
1 + ----------------------
2
sec (a)
$$\frac{\left(-1 + \frac{1}{\sec^{2}{\left(a \right)}}\right) \csc^{2}{\left(a \right)}}{\sec^{2}{\left(a \right)}} + 1$$
4 / 1 \
csc (a)*|-1 + -------|
| 2 |
\ sec (a)/
1 + ----------------------
2
4*csc (2*a)
$$\frac{\left(-1 + \frac{1}{\sec^{2}{\left(a \right)}}\right) \csc^{4}{\left(a \right)}}{4 \csc^{2}{\left(2 a \right)}} + 1$$
2 / 2 \
cos (a)*\-1 + cos (a)/
1 + ----------------------
2/ pi\
cos |a - --|
\ 2 /
$$\frac{\left(\cos^{2}{\left(a \right)} - 1\right) \cos^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}} + 1$$
2 / 2/ pi\\
sin (2*a)*|-1 + sin |a + --||
\ \ 2 //
1 + -----------------------------
4
4*sin (a)
$$1 + \frac{\left(\sin^{2}{\left(a + \frac{\pi}{2} \right)} - 1\right) \sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}$$
/ 2 2 \
2 | 1 cos (a) sin (a)|
1 + cot (a)*|- - + ------- - -------|
\ 2 2 2 /
$$\left(- \frac{\sin^{2}{\left(a \right)}}{2} + \frac{\cos^{2}{\left(a \right)}}{2} - \frac{1}{2}\right) \cot^{2}{\left(a \right)} + 1$$
2/ pi\ / 1 \
sec |a - --|*|-1 + -------|
\ 2 / | 2 |
\ sec (a)/
1 + ---------------------------
2
sec (a)
$$\frac{\left(-1 + \frac{1}{\sec^{2}{\left(a \right)}}\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}} + 1$$
2/pi \ / 1 \
sec |-- - a|*|-1 + -------|
\2 / | 2 |
\ sec (a)/
1 + ---------------------------
2
sec (a)
$$\frac{\left(-1 + \frac{1}{\sec^{2}{\left(a \right)}}\right) \sec^{2}{\left(- a + \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}} + 1$$
2
/ 2/a\\ 2
|1 - tan |-|| *sin (a)
\ \2//
1 - ----------------------
2/a\
4*tan |-|
\2/
$$- \frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \sin^{2}{\left(a \right)}}{4 \tan^{2}{\left(\frac{a}{2} \right)}} + 1$$
2/ pi\ / 2/ pi\\
sin |a + --|*|-1 + sin |a + --||
\ 2 / \ \ 2 //
1 + --------------------------------
2
sin (a)
$$\frac{\left(\sin^{2}{\left(a + \frac{\pi}{2} \right)} - 1\right) \sin^{2}{\left(a + \frac{\pi}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1$$
2/ pi\ / 2 \
cos |2*a - --|*\-1 + cos (a)/
\ 2 /
1 + -----------------------------
4/ pi\
4*cos |a - --|
\ 2 /
$$1 + \frac{\left(\cos^{2}{\left(a \right)} - 1\right) \cos^{2}{\left(2 a - \frac{\pi}{2} \right)}}{4 \cos^{4}{\left(a - \frac{\pi}{2} \right)}}$$
4/ pi\ / 1 \
sec |a - --|*|-1 + -------|
\ 2 / | 2 |
\ sec (a)/
1 + ---------------------------
2/ pi\
4*sec |2*a - --|
\ 2 /
$$\frac{\left(-1 + \frac{1}{\sec^{2}{\left(a \right)}}\right) \sec^{4}{\left(a - \frac{\pi}{2} \right)}}{4 \sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} + 1$$
2 / 1 \
csc (a)*|-1 + ------------|
| 2/pi \|
| csc |-- - a||
\ \2 //
1 + ---------------------------
2/pi \
csc |-- - a|
\2 /
$$\frac{\left(-1 + \frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + 1$$
2 / 1 \
csc (pi - a)*|-1 + ------------|
| 2/pi \|
| csc |-- - a||
\ \2 //
1 + --------------------------------
2/pi \
csc |-- - a|
\2 /
$$\frac{\left(-1 + \frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(- a + \pi \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + 1$$
2 4/a\
16*cos (a)*sin |-|
\2/
1 - ----------------------
2
/ 2 4/a\\
|sin (a) + 4*sin |-||
\ \2//
$$- \frac{16 \sin^{4}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)}}{\left(4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}} + 1$$
2
/ 2/a\\
|1 - tan |-||
\ \2//
-1 + --------------
2
/ 2/a\\
|1 + tan |-||
\ \2//
1 + -------------------
2
tan (a)
$$1 + \frac{\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - 1}{\tan^{2}{\left(a \right)}}$$
// 1 for a mod 2*pi = 0\
|| |
-1 + |< 2 |
||cos (a) otherwise |
\\ /
1 + -----------------------------------
2
tan (a)
$$1 + \left(\frac{\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) - 1}{\tan^{2}{\left(a \right)}}\right)$$
/ // 1 for a mod 2*pi = 0\\
2 | || ||
1 + cot (a)*|-1 + |< 2 ||
| ||cos (a) otherwise ||
\ \\ //
$$\left(\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) - 1\right) \cot^{2}{\left(a \right)}\right) + 1$$
/ 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\
| / 1 \ |
| |1 - -------| |
| | 2/a\| |
| | cot |-|| |
2 | \ \2// |
1 + cot (a)*|-1 + --------------|
| 2|
| / 1 \ |
| |1 + -------| |
| | 2/a\| |
| | cot |-|| |
\ \ \2// /
$$\left(\frac{\left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} - 1\right) \cot^{2}{\left(a \right)} + 1$$
/ // 1 for a mod 2*pi = 0\\
2 | || ||
cos (a)*|-1 + |< 2 ||
| ||cos (a) otherwise ||
\ \\ //
1 + ---------------------------------------------
2/ pi\
cos |a - --|
\ 2 /
$$\left(\frac{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) - 1\right) \cos^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}\right) + 1$$
/ // 1 for a mod 2*pi = 0\\
2 | || ||
sin (2*a)*|-1 + |< 2/ pi\ ||
| ||sin |a + --| otherwise ||
\ \\ \ 2 / //
1 + ----------------------------------------------------
4
4*sin (a)
$$1 + \left(\frac{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\sin^{2}{\left(a + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) - 1\right) \sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}\right)$$
/ // 1 for a mod 2*pi = 0\\
| || ||
2/ pi\ | || 1 ||
sec |a - --|*|-1 + |<------- otherwise ||
\ 2 / | || 2 ||
| ||sec (a) ||
\ \\ //
1 + --------------------------------------------------
2
sec (a)
$$\left(\frac{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\sec^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right) - 1\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}}\right) + 1$$
/ 2\
| / 2/a\\ |
2 | |1 - tan |-|| |
/ 2/a\\ | \ \2// |
|1 - tan |-|| *|-1 + --------------|
\ \2// | 2|
| / 2/a\\ |
| |1 + tan |-|| |
\ \ \2// /
1 + ------------------------------------
2/a\
4*tan |-|
\2/
$$\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - 1\right)}{4 \tan^{2}{\left(\frac{a}{2} \right)}} + 1$$
2
/ 2/a\\ 4/a\ 2
4*|1 - tan |-|| *cos |-|*sin (a)
\ \2// \2/
1 - ---------------------------------
2
/ 2/a pi\\ 2
|1 - cot |- + --|| *(1 + sin(a))
\ \2 4 //
$$- \frac{4 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \sin^{2}{\left(a \right)} \cos^{4}{\left(\frac{a}{2} \right)}}{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\sin{\left(a \right)} + 1\right)^{2}} + 1$$
/ // 1 for a mod 2*pi = 0\\
| || ||
2 | || 1 ||
csc (a)*|-1 + |<------------ otherwise ||
| || 2/pi \ ||
| ||csc |-- - a| ||
\ \\ \2 / //
1 + --------------------------------------------------
2/pi \
csc |-- - a|
\2 /
$$\left(\frac{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) - 1\right) \csc^{2}{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}\right) + 1$$
/ // 1 for a mod 2*pi = 0\\
| || ||
2 | ||/ 1 for a mod 2*pi = 0 ||
1 + cot (a)*|-1 + |<| ||
| ||< 2 otherwise ||
| |||cos (a) otherwise ||
\ \\\ //
$$\left(\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) - 1\right) \cot^{2}{\left(a \right)}\right) + 1$$
// 1 for a mod 2*pi = 0\
|| |
|| 2 |
||/ 2/a\\ |
|||1 - tan |-|| |
-1 + |<\ \2// |
||-------------- otherwise |
|| 2 |
||/ 2/a\\ |
|||1 + tan |-|| |
\\\ \2// /
1 + ------------------------------------------
2
tan (a)
$$1 + \left(\frac{\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1}{\tan^{2}{\left(a \right)}}\right)$$
/ // 1 for a mod 2*pi = 0\\
| || ||
| || 2 ||
| ||/ 2/a\\ ||
2 | |||-1 + cot |-|| ||
1 + cot (a)*|-1 + |<\ \2// ||
| ||--------------- otherwise ||
| || 2 ||
| || / 2/a\\ ||
| || |1 + cot |-|| ||
\ \\ \ \2// //
$$\left(\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1\right) \cot^{2}{\left(a \right)}\right) + 1$$
/ 2\
| / 4/a\\ |
| | 4*sin |-|| |
| | \2/| |
| |1 - ---------| |
| | 2 | |
2 | \ sin (a) / |
sin (2*a)*|-1 + ----------------|
| 2|
| / 4/a\\ |
| | 4*sin |-|| |
| | \2/| |
| |1 + ---------| |
| | 2 | |
\ \ sin (a) / /
1 + ---------------------------------
4
4*sin (a)
$$1 + \frac{\left(\frac{\left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2}} - 1\right) \sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}$$
// 1 for a mod 2*pi = 0\
|| |
|| 2 |
||/ 1 \ |
|||-1 + -------| |
||| 2/a\| |
||| tan |-|| |
-1 + |<\ \2// |
||--------------- otherwise |
|| 2 |
|| / 1 \ |
|| |1 + -------| |
|| | 2/a\| |
|| | tan |-|| |
\\ \ \2// /
1 + -------------------------------------------
2
tan (a)
$$1 + \left(\frac{\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right) - 1}{\tan^{2}{\left(a \right)}}\right)$$
// 1 for a mod 2*pi = 0\
|| |
|| 2 |
||/ 2 4/a\\ |
|||sin (a) - 4*sin |-|| |
-1 + |<\ \2// |
||---------------------- otherwise |
|| 2 |
||/ 2 4/a\\ |
|||sin (a) + 4*sin |-|| |
\\\ \2// /
1 + --------------------------------------------------
2
tan (a)
$$1 + \left(\frac{\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(- 4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}}{\left(4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}} & \text{otherwise} \end{cases}\right) - 1}{\tan^{2}{\left(a \right)}}\right)$$
/ 2/a pi\ \
4 | 4*tan |- + --| |
/ 2/a\\ 2 | \2 4 / |
|1 + tan |-|| *tan (a)*|-1 + -------------------|
\ \2// | 2|
| / 2/a pi\\ |
| |1 + tan |- + --|| |
\ \ \2 4 // /
1 + -------------------------------------------------
2
/ 2 \ 4/a\
16*\1 + tan (a)/ *tan |-|
\2/
$$\frac{\left(-1 + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{4} \tan^{2}{\left(a \right)}}{16 \left(\tan^{2}{\left(a \right)} + 1\right)^{2} \tan^{4}{\left(\frac{a}{2} \right)}} + 1$$
/ 2\
| / 2/a pi\\ |
| | cos |- - --|| |
| | \2 2 /| |
| |1 - ------------| |
| | 2/a\ | |
| | cos |-| | |
2 | \ \2/ / |
cos (a)*|-1 + -------------------|
| 2|
| / 2/a pi\\ |
| | cos |- - --|| |
| | \2 2 /| |
| |1 + ------------| |
| | 2/a\ | |
| | cos |-| | |
\ \ \2/ / /
1 + ----------------------------------
2/ pi\
cos |a - --|
\ 2 /
$$\frac{\left(\frac{\left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} - 1\right) \cos^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}} + 1$$
/ 2\
| / 2/a\ \ |
| | sec |-| | |
| | \2/ | |
| |1 - ------------| |
| | 2/a pi\| |
| | sec |- - --|| |
2/ pi\ | \ \2 2 // |
sec |a - --|*|-1 + -------------------|
\ 2 / | 2|
| / 2/a\ \ |
| | sec |-| | |
| | \2/ | |
| |1 + ------------| |
| | 2/a pi\| |
| | sec |- - --|| |
\ \ \2 2 // /
1 + ---------------------------------------
2
sec (a)
$$\frac{\left(\frac{\left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}} - 1\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}} + 1$$
/ 2\
| / 2/pi a\\ |
| | csc |-- - -|| |
| | \2 2/| |
| |1 - ------------| |
| | 2/a\ | |
| | csc |-| | |
2 | \ \2/ / |
csc (a)*|-1 + -------------------|
| 2|
| / 2/pi a\\ |
| | csc |-- - -|| |
| | \2 2/| |
| |1 + ------------| |
| | 2/a\ | |
| | csc |-| | |
\ \ \2/ / /
1 + ----------------------------------
2/pi \
csc |-- - a|
\2 /
$$\frac{\left(\frac{\left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} - 1\right) \csc^{2}{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + 1$$
/ // 1 for a mod 2*pi = 0\\
| || ||
| ||/ 1 for a mod 2*pi = 0 ||
| ||| ||
| ||| 2 ||
2 | |||/ 2/a\\ ||
1 + cot (a)*|-1 + |<||-1 + cot |-|| ||
| ||<\ \2// otherwise ||
| |||--------------- otherwise ||
| ||| 2 ||
| ||| / 2/a\\ ||
| ||| |1 + cot |-|| ||
\ \\\ \ \2// //
$$\left(\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) - 1\right) \cot^{2}{\left(a \right)}\right) + 1$$
/ 2/a pi\ \
2 | 4*tan |- + --| |
/ 2/a\\ 2/a pi\ | \2 4 / |
|1 + cot |-|| *tan |- + --|*|-1 + -------------------|
\ \2// \2 4 / | 2|
| / 2/a pi\\ |
| |1 + tan |- + --|| |
\ \ \2 4 // /
1 + ------------------------------------------------------
2
/ 2/a pi\\ 2/a\
|1 + tan |- + --|| *cot |-|
\ \2 4 // \2/
$$\frac{\left(-1 + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{a}{2} \right)}} + 1$$
/ // 1 for a mod 2*pi = 0\\
| || ||
| || 2 ||
| ||/ 2 \ ||
| ||| sin (a) | ||
| |||-1 + ---------| ||
| ||| 4/a\| ||
2 | ||| 4*sin |-|| ||
sin (2*a)*|-1 + |<\ \2// ||
| ||----------------- otherwise ||
| || 2 ||
| || / 2 \ ||
| || | sin (a) | ||
| || |1 + ---------| ||
| || | 4/a\| ||
| || | 4*sin |-|| ||
\ \\ \ \2// //
1 + ---------------------------------------------------------
4
4*sin (a)
$$1 + \left(\frac{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right) - 1\right) \sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}\right)$$
/ 2\
| / 2/a\\ |
2 2 | |-1 + cot |-|| |
/ 2/a pi\\ / 2/a\\ | \ \2// |
|1 + tan |- + --|| *|-1 + cot |-|| *|-1 + ---------------|
\ \2 4 // \ \2// | 2|
| / 2/a\\ |
| |1 + cot |-|| |
\ \ \2// /
1 + ----------------------------------------------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + cot |-|| *|-1 + tan |- + --||
\ \2// \ \2 4 //
$$\frac{\left(\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + 1$$
/ 2\
| / 2/a\\ |
2 2 | |1 - tan |-|| |
/ 2/a pi\\ / 2/a\\ | \ \2// |
|1 + cot |- + --|| *|1 - tan |-|| *|-1 + --------------|
\ \2 4 // \ \2// | 2|
| / 2/a\\ |
| |1 + tan |-|| |
\ \ \2// /
1 + --------------------------------------------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + tan |-|| *|1 - cot |- + --||
\ \2// \ \2 4 //
$$\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + 1$$
/ // 1 for a mod 2*pi = 0\\
| || ||
| || 2 ||
| ||/ 2/a\ \ ||
| ||| cos |-| | ||
| ||| \2/ | ||
| |||-1 + ------------| ||
| ||| 2/a pi\| ||
2 | ||| cos |- - --|| ||
cos (a)*|-1 + |<\ \2 2 // ||
| ||-------------------- otherwise ||
| || 2 ||
| ||/ 2/a\ \ ||
| ||| cos |-| | ||
| ||| \2/ | ||
| |||1 + ------------| ||
| ||| 2/a pi\| ||
| ||| cos |- - --|| ||
\ \\\ \2 2 // //
1 + ----------------------------------------------------------
2/ pi\
cos |a - --|
\ 2 /
$$\left(\frac{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1\right) \cos^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}\right) + 1$$
/ // 1 for a mod 2*pi = 0\\
| || ||
| || 2 ||
| ||/ 2/a pi\\ ||
| ||| sec |- - --|| ||
| ||| \2 2 /| ||
| |||-1 + ------------| ||
| ||| 2/a\ | ||
2/ pi\ | ||| sec |-| | ||
sec |a - --|*|-1 + |<\ \2/ / ||
\ 2 / | ||-------------------- otherwise ||
| || 2 ||
| ||/ 2/a pi\\ ||
| ||| sec |- - --|| ||
| ||| \2 2 /| ||
| |||1 + ------------| ||
| ||| 2/a\ | ||
| ||| sec |-| | ||
\ \\\ \2/ / //
1 + ---------------------------------------------------------------
2
sec (a)
$$\left(\frac{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right) - 1\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}}\right) + 1$$
/ // 1 for a mod 2*pi = 0\\
| || ||
| || 2 ||
| ||/ 2/a\ \ ||
| ||| csc |-| | ||
| ||| \2/ | ||
| |||-1 + ------------| ||
| ||| 2/pi a\| ||
2 | ||| csc |-- - -|| ||
csc (a)*|-1 + |<\ \2 2// ||
| ||-------------------- otherwise ||
| || 2 ||
| ||/ 2/a\ \ ||
| ||| csc |-| | ||
| ||| \2/ | ||
| |||1 + ------------| ||
| ||| 2/pi a\| ||
| ||| csc |-- - -|| ||
\ \\\ \2 2// //
1 + ----------------------------------------------------------
2/pi \
csc |-- - a|
\2 /
$$\left(\frac{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1\right) \csc^{2}{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}\right) + 1$$
// / 3*pi\ \
|| 1 for |a + ----| mod 2*pi = 0|
|| \ 2 / |
|| |
/ // 1 for a mod 2*pi = 0\\ // 1 for a mod 2*pi = 0\ || 1 |
| || || || | ||-1 + ------- |
1 + |-1 + |< 2 ||*|< 2 |*|< 2/a\ |
| ||cos (a) otherwise || ||cos (a) otherwise | || sin |-| |
\ \\ // \\ / || \2/ |
||------------ otherwise |
|| 4/a\ |
|| 4*cos |-| |
\\ \2/ /
$$\left(\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) - 1\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\sin^{2}{\left(\frac{a}{2} \right)}}}{4 \cos^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1$$
// zoo for a mod pi = 0\
/ // / pi\ \\ || |
| || 0 for |a + --| mod pi = 0|| // 0 for 2*a mod pi = 0\ || 4/a\ |
| || \ 2 / || || | || tan |-| |
|-1 + |< ||*|<1 - cos(4*a) |*|< \2/ |
| || 2 2/a pi\ || ||------------ otherwise | ||---------- otherwise |
| ||(1 + sin(a)) *cot |- + --| otherwise || \\ 2 / || 8/a\ |
\ \\ \2 4 / // ||16*sin |-| |
\\ \2/ /
1 + ---------------------------------------------------------------------------------------------------------------------------------
4
$$\left(\frac{\left(\left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(a \right)} + 1\right)^{2} \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right) - 1\right) \left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{- \cos{\left(4 a \right)} + 1}{2} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: a \bmod \pi = 0 \\\frac{\tan^{4}{\left(\frac{a}{2} \right)}}{16 \sin^{8}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)}{4}\right) + 1$$
/ // / pi\ \\
| || 0 for |a + --| mod pi = 0|| // zoo for a mod pi = 0\
| || \ 2 / || // 0 for 2*a mod pi = 0\ || |
| || || || | || 4 |
| || 2/a pi\ || || 2 | ||/ 2/a\\ |
| || 4*cot |- + --| || || 4*cot (a) | |||1 + cot |-|| |
|-1 + |< \2 4 / ||*|<-------------- otherwise |*|<\ \2// |
| ||------------------- otherwise || || 2 | ||-------------- otherwise |
| || 2 || ||/ 2 \ | || 4/a\ |
| ||/ 2/a pi\\ || ||\1 + cot (a)/ | || 16*cot |-| |
| |||1 + cot |- + --|| || \\ / || \2/ |
| ||\ \2 4 // || \\ /
\ \\ //
1 + --------------------------------------------------------------------------------------------------------------------------------
4
$$\left(\frac{\left(\left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1\right) \left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(a \right)}}{\left(\cot^{2}{\left(a \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: a \bmod \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{4}}{16 \cot^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)}{4}\right) + 1$$
// / 3*pi\ \
/ // 1 for a mod 2*pi = 0\\ // 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
| || || || | || \ 2 / |
| || 2 || || 2 | || |
| ||/ 2/a\\ || ||/ 2/a\\ | || 2 |
| |||-1 + cot |-|| || |||-1 + cot |-|| | ||/ 2/a pi\\ |
1 + |-1 + |<\ \2// ||*|<\ \2// |*|<|1 + tan |- + --|| |
| ||--------------- otherwise || ||--------------- otherwise | ||\ \2 4 // |
| || 2 || || 2 | ||-------------------- otherwise |
| || / 2/a\\ || || / 2/a\\ | || 2 |
| || |1 + cot |-|| || || |1 + cot |-|| | ||/ 2/a pi\\ |
\ \\ \ \2// // \\ \ \2// / |||-1 + tan |- + --|| |
\\\ \2 4 // /
$$\left(\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1\right) \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1$$
1 + (-1 + Piecewise((1, Mod(a = 2*pi, 0)), ((-1 + cot(a/2)^2)^2/(1 + cot(a/2)^2)^2, True)))*Piecewise((1, Mod(a = 2*pi, 0)), ((-1 + cot(a/2)^2)^2/(1 + cot(a/2)^2)^2, True))*Piecewise((1, Mod(a + 3*pi/2 = 2*pi, 0)), ((1 + tan(a/2 + pi/4)^2)^2/(-1 + tan(a/2 + pi/4)^2)^2, True))