Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- x^2+3*x^2 если x=-1/3
- (1-c)*(c-1) если c=3/2
- cos(l-b)-cos(l+b) если b=1/2
- c+5*c если c=4
- Разложить многочлен на множители:
- x^2+16*x+15
- 1-6*c^2+9*c^4
- 63*y^3-84*y^2*z+28*y*z^2
- 42*a*m+30*m*u-18*a*u-70*m^2
- Общий знаменатель:
- ((x^2-25)/(x+6))*(1/(x^2+5*x))-((x+5)/(x^2-6*x))
- (15-8*a)/(a-1)^2-(14-7*a)/(1-a)^2
- 5*a+10/b-7/a^2+4*a+4/2*b+14
- (49*b^2-4)*(1/(7*b-2)-1/(7*b+2))-b+15
- Умножение столбиком:
- 815*204
- 25*50
- 48*3200
- 12*35
- Деление столбиком:
- 147/2
- 6036/4
- 888/3
- 165/8
- Раскрыть скобки в:
- (y+3)*(y+3)-(y-3)*(y-3)
- 7*(5*a+8)-11*a
- (x-1)^2*(x+1)^2*(x^2+1)^2
- (2*p-3)*(2*p+3)-11
- Разложение числа на простые множители:
- 4140
- 56
- 2097
- 2484
- График функции y =:
- 1/2
- Производная:
- 1/2
- Интеграл d{x}:
-
1/2
-
Идентичные выражения
- cos(l-b)-cos(l+b) если b= один / два
- косинус от (l минус b) минус косинус от (l плюс b) если b равно 1 делить на 2
- косинус от (l минус b) минус косинус от (l плюс b) если b равно один делить на два
- cosl-b-cosl+b если b=1/2
- cos(l-b)-cos(l+b) при b=1/2
- cos(l-b)-cos(l+b) если b=1 разделить на 2
-
Похожие выражения
- (s-1)/2+(s-1)/2 если s=1/3
- cos(l-b)-cos(l-b) если b=1/2
- cos(l+b)-cos(l+b) если b=1/2
- cos(l-b)+cos(l+b) если b=1/2
cos(l-b)-cos(l+b) если b=1/2
Решение
Вы ввели
[src]
cos(l - b) - cos(l + b)
$$\cos{\left(- b + l \right)} - \cos{\left(b + l \right)}$$
cos(l - b) - cos(l + b)
Общее упрощение
[src]
2*sin(b)*sin(l)
$$2 \sin{\left(b \right)} \sin{\left(l \right)}$$
2*sin(b)*sin(l)
Подстановка условия
[src]
cos(l - b) - cos(l + b) при b = 1/2
подставляем
cos(l - b) - cos(l + b)
$$\cos{\left(- b + l \right)} - \cos{\left(b + l \right)}$$
2*sin(b)*sin(l)
$$2 \sin{\left(b \right)} \sin{\left(l \right)}$$
переменные
b = 1/2
$$b = \frac{1}{2}$$
2*sin((1/2))*sin(l)
$$2 \sin{\left((1/2) \right)} \sin{\left(l \right)}$$
2*sin(1/2)*sin(l)
$$2 \sin{\left(\frac{1}{2} \right)} \sin{\left(l \right)}$$
2*sin(1/2)*sin(l)
Собрать выражение
[src]
-cos(b + l) + cos(b - l)
$$\cos{\left(b - l \right)} - \cos{\left(b + l \right)}$$
-cos(b + l) + cos(b - l)
Тригонометрическая часть
[src]
2*sin(b)*sin(l)
$$2 \sin{\left(b \right)} \sin{\left(l \right)}$$
-cos(b + l) + cos(b - l)
$$\cos{\left(b - l \right)} - \cos{\left(b + l \right)}$$
2 ------------- csc(b)*csc(l)
$$\frac{2}{\csc{\left(b \right)} \csc{\left(l \right)}}$$
1 1 ---------- - ---------- sec(b - l) sec(b + l)
$$- \frac{1}{\sec{\left(b + l \right)}} + \frac{1}{\sec{\left(b - l \right)}}$$
/ pi\ / pi\
2*cos|b - --|*cos|l - --|
\ 2 / \ 2 /
$$2 \cos{\left(b - \frac{\pi}{2} \right)} \cos{\left(l - \frac{\pi}{2} \right)}$$
2 ----------------------- / pi\ / pi\ sec|b - --|*sec|l - --| \ 2 / \ 2 /
$$\frac{2}{\sec{\left(b - \frac{\pi}{2} \right)} \sec{\left(l - \frac{\pi}{2} \right)}}$$
/ pi\ / pi \
- sin|b + l + --| + sin|b + -- - l|
\ 2 / \ 2 /
$$\sin{\left(b - l + \frac{\pi}{2} \right)} - \sin{\left(b + l + \frac{\pi}{2} \right)}$$
1 1 --------------- - --------------- / pi \ /pi \ csc|l + -- - b| csc|-- - b - l| \ 2 / \2 /
$$\frac{1}{\csc{\left(- b + l + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(- b - l + \frac{\pi}{2} \right)}}$$
/b\ /l\ /b\ /l\
8*cos|-|*cos|-|*sin|-|*sin|-|
\2/ \2/ \2/ \2/
$$8 \sin{\left(\frac{b}{2} \right)} \sin{\left(\frac{l}{2} \right)} \cos{\left(\frac{b}{2} \right)} \cos{\left(\frac{l}{2} \right)}$$
/b\ /l\ /pi b\ /pi l\
8*sin|-|*sin|-|*sin|-- + -|*sin|-- + -|
\2/ \2/ \2 2/ \2 2/
$$8 \sin{\left(\frac{b}{2} \right)} \sin{\left(\frac{l}{2} \right)} \sin{\left(\frac{b}{2} + \frac{\pi}{2} \right)} \sin{\left(\frac{l}{2} + \frac{\pi}{2} \right)}$$
/b\ /l\ /b pi\ /l pi\
8*cos|-|*cos|-|*cos|- - --|*cos|- - --|
\2/ \2/ \2 2 / \2 2 /
$$8 \cos{\left(\frac{b}{2} \right)} \cos{\left(\frac{l}{2} \right)} \cos{\left(\frac{b}{2} - \frac{\pi}{2} \right)} \cos{\left(\frac{l}{2} - \frac{\pi}{2} \right)}$$
8 ------------------------------------- /b\ /l\ /b pi\ /l pi\ sec|-|*sec|-|*sec|- - --|*sec|- - --| \2/ \2/ \2 2 / \2 2 /
$$\frac{8}{\sec{\left(\frac{b}{2} \right)} \sec{\left(\frac{l}{2} \right)} \sec{\left(\frac{b}{2} - \frac{\pi}{2} \right)} \sec{\left(\frac{l}{2} - \frac{\pi}{2} \right)}}$$
8 ------------------------------------- /b\ /l\ /pi b\ /pi l\ csc|-|*csc|-|*csc|-- - -|*csc|-- - -| \2/ \2/ \2 2/ \2 2/
$$\frac{8}{\csc{\left(\frac{b}{2} \right)} \csc{\left(\frac{l}{2} \right)} \csc{\left(- \frac{b}{2} + \frac{\pi}{2} \right)} \csc{\left(- \frac{l}{2} + \frac{\pi}{2} \right)}}$$
/b\ /l\
8*tan|-|*tan|-|
\2/ \2/
---------------------------
/ 2/b\\ / 2/l\\
|1 + tan |-||*|1 + tan |-||
\ \2// \ \2//
$$\frac{8 \tan{\left(\frac{b}{2} \right)} \tan{\left(\frac{l}{2} \right)}}{\left(\tan^{2}{\left(\frac{b}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{l}{2} \right)} + 1\right)}$$
// 0 for b mod pi = 0\ // 0 for l mod pi = 0\ 2*|< |*|< | \\sin(b) otherwise / \\sin(l) otherwise /
$$2 \left(\begin{cases} 0 & \text{for}\: b \bmod \pi = 0 \\\sin{\left(b \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: l \bmod \pi = 0 \\\sin{\left(l \right)} & \text{otherwise} \end{cases}\right)$$
2/b l\ 2/b l\
-1 + cot |- - -| -1 + cot |- + -|
\2 2/ \2 2/
---------------- - ----------------
2/b l\ 2/b l\
1 + cot |- - -| 1 + cot |- + -|
\2 2/ \2 2/
$$\frac{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} + 1} - \frac{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} + 1}$$
2/b l\ 2/b l\
1 - tan |- - -| 1 - tan |- + -|
\2 2/ \2 2/
--------------- - ---------------
2/b l\ 2/b l\
1 + tan |- - -| 1 + tan |- + -|
\2 2/ \2 2/
$$\frac{- \tan^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} + 1}{\tan^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} + 1} - \frac{- \tan^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} + 1}{\tan^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} + 1}$$
/b l pi\
2*tan|- + - + --|
/l b pi\ \2 2 4 /
(1 - sin(b - l))*cot|- - - + --| - --------------------
\2 2 4 / 2/b l pi\
1 + tan |- + - + --|
\2 2 4 /
$$\left(- \sin{\left(b - l \right)} + 1\right) \cot{\left(- \frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)} - \frac{2 \tan{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)} + 1}$$
4/b\ 4/l\ / 2/b\\ / 2/l\\ /b\ /l\
32*cos |-|*cos |-|*|1 - tan |-||*|1 - tan |-||*tan|-|*tan|-|
\4/ \4/ \ \4// \ \4// \4/ \4/
$$32 \cdot \left(- \tan^{2}{\left(\frac{b}{4} \right)} + 1\right) \left(- \tan^{2}{\left(\frac{l}{4} \right)} + 1\right) \cos^{4}{\left(\frac{b}{4} \right)} \cos^{4}{\left(\frac{l}{4} \right)} \tan{\left(\frac{b}{4} \right)} \tan{\left(\frac{l}{4} \right)}$$
1 1
1 - ----------- 1 - -----------
2/b l\ 2/b l\
cot |- - -| cot |- + -|
\2 2/ \2 2/
--------------- - ---------------
1 1
1 + ----------- 1 + -----------
2/b l\ 2/b l\
cot |- - -| cot |- + -|
\2 2/ \2 2/
$$\frac{1 - \frac{1}{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}}{1 + \frac{1}{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}} - \frac{1 - \frac{1}{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}{1 + \frac{1}{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ - |< | + |< | \\cos(b + l) otherwise / \\cos(b - l) otherwise /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\cos{\left(b - l \right)} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\cos{\left(b + l \right)} & \text{otherwise} \end{cases}\right)$$
/b l pi\ /b l pi\
2*tan|- + - + --| 2*tan|- - - + --|
\2 2 4 / \2 2 4 /
- -------------------- + --------------------
2/b l pi\ 2/b l pi\
1 + tan |- + - + --| 1 + tan |- - - + --|
\2 2 4 / \2 2 4 /
$$- \frac{2 \tan{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)} + 1} + \frac{2 \tan{\left(\frac{b}{2} - \frac{l}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{b}{2} - \frac{l}{2} + \frac{\pi}{4} \right)} + 1}$$
/b l pi\ /l b pi\
2*tan|- + - + --| 2*cot|- - - + --|
\2 2 4 / \2 2 4 /
- -------------------- + --------------------
2/b l pi\ 2/l b pi\
1 + tan |- + - + --| 1 + cot |- - - + --|
\2 2 4 / \2 2 4 /
$$\frac{2 \cot{\left(- \frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(- \frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)} + 1} - \frac{2 \tan{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)} + 1}$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | - |< 1 | + |< 1 | ||---------- otherwise | ||---------- otherwise | \\sec(b + l) / \\sec(b - l) /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(b - l \right)}} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(b + l \right)}} & \text{otherwise} \end{cases}\right)$$
/ 2/b\\ / 2/l\\ /b\ /l\
32*|1 - tan |-||*|1 - tan |-||*tan|-|*tan|-|
\ \4// \ \4// \4/ \4/
--------------------------------------------
2 2
/ 2/b\\ / 2/l\\
|1 + tan |-|| *|1 + tan |-||
\ \4// \ \4//
$$\frac{32 \cdot \left(- \tan^{2}{\left(\frac{b}{4} \right)} + 1\right) \left(- \tan^{2}{\left(\frac{l}{4} \right)} + 1\right) \tan{\left(\frac{b}{4} \right)} \tan{\left(\frac{l}{4} \right)}}{\left(\tan^{2}{\left(\frac{b}{4} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{l}{4} \right)} + 1\right)^{2}}$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | - |< / pi\ | + |< / pi \ | ||sin|b + l + --| otherwise | ||sin|b + -- - l| otherwise | \\ \ 2 / / \\ \ 2 / /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\sin{\left(b - l + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\sin{\left(b + l + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | || 1 | || 1 | - |<--------------- otherwise | + |<--------------- otherwise | || /pi \ | || / pi \ | ||csc|-- - b - l| | ||csc|l + -- - b| | \\ \2 / / \\ \ 2 / /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- b + l + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- b - l + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for b mod pi = 0\ // 0 for l mod pi = 0\ || | || | || /b\ | || /l\ | || 2*cot|-| | || 2*cot|-| | 2*|< \2/ |*|< \2/ | ||----------- otherwise | ||----------- otherwise | || 2/b\ | || 2/l\ | ||1 + cot |-| | ||1 + cot |-| | \\ \2/ / \\ \2/ /
$$2 \left(\begin{cases} 0 & \text{for}\: b \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{b}{2} \right)}}{\cot^{2}{\left(\frac{b}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: l \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{l}{2} \right)}}{\cot^{2}{\left(\frac{l}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
4/b - l\ 4/b + l\
4*sin |-----| 4*sin |-----|
\ 2 / \ 2 /
1 - ------------- 1 - -------------
2 2
sin (b - l) sin (b + l)
----------------- - -----------------
4/b - l\ 4/b + l\
4*sin |-----| 4*sin |-----|
\ 2 / \ 2 /
1 + ------------- 1 + -------------
2 2
sin (b - l) sin (b + l)
$$\frac{- \frac{4 \sin^{4}{\left(\frac{b - l}{2} \right)}}{\sin^{2}{\left(b - l \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{b - l}{2} \right)}}{\sin^{2}{\left(b - l \right)}} + 1} - \frac{- \frac{4 \sin^{4}{\left(\frac{b + l}{2} \right)}}{\sin^{2}{\left(b + l \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{b + l}{2} \right)}}{\sin^{2}{\left(b + l \right)}} + 1}$$
4/b l\ 4/b l\
4*sin |- - -| 4*sin |- + -|
\2 2/ \2 2/
1 - ------------- 1 - -------------
2 2
sin (b - l) sin (b + l)
----------------- - -----------------
4/b l\ 4/b l\
4*sin |- - -| 4*sin |- + -|
\2 2/ \2 2/
1 + ------------- 1 + -------------
2 2
sin (b - l) sin (b + l)
$$\frac{- \frac{4 \sin^{4}{\left(\frac{b}{2} - \frac{l}{2} \right)}}{\sin^{2}{\left(b - l \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{b}{2} - \frac{l}{2} \right)}}{\sin^{2}{\left(b - l \right)}} + 1} - \frac{- \frac{4 \sin^{4}{\left(\frac{b}{2} + \frac{l}{2} \right)}}{\sin^{2}{\left(b + l \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{b}{2} + \frac{l}{2} \right)}}{\sin^{2}{\left(b + l \right)}} + 1}$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | || 2/b l\ | || 2/b l\ | ||-1 + cot |- + -| | ||-1 + cot |- - -| | - |< \2 2/ | + |< \2 2/ | ||---------------- otherwise | ||---------------- otherwise | || 2/b l\ | || 2/b l\ | ||1 + cot |- + -| | ||1 + cot |- - -| | \\ \2 2/ / \\ \2 2/ /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | || 2/b l\ | || 2/b l\ | ||1 - tan |- + -| | ||1 - tan |- - -| | - |< \2 2/ | + |< \2 2/ | ||--------------- otherwise | ||--------------- otherwise | || 2/b l\ | || 2/b l\ | ||1 + tan |- + -| | ||1 + tan |- - -| | \\ \2 2/ / \\ \2 2/ /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} + 1}{\tan^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} + 1}{\tan^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// / pi\ \ // / pi \ \ || 0 for |b + l + --| mod pi = 0| || 0 for |b + -- - l| mod pi = 0| || \ 2 / | || \ 2 / | - |< | + |< | || /b l pi\ | || /b l pi\ | ||(1 + sin(b + l))*cot|- + - + --| otherwise | ||(1 + sin(b - l))*cot|- - - + --| otherwise | \\ \2 2 4 / / \\ \2 2 4 / /
$$\left(\begin{cases} 0 & \text{for}\: \left(b - l + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(b - l \right)} + 1\right) \cot{\left(\frac{b}{2} - \frac{l}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 0 & \text{for}\: \left(b + l + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(b + l \right)} + 1\right) \cot{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\
|| | || |
- |
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\cos{\left(b - l \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\cos{\left(b + l \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | || 1 | || 1 | ||-1 + ----------- | ||-1 + ----------- | || 2/b l\ | || 2/b l\ | || tan |- + -| | || tan |- - -| | - |< \2 2/ | + |< \2 2/ | ||---------------- otherwise | ||---------------- otherwise | || 1 | || 1 | ||1 + ----------- | ||1 + ----------- | || 2/b l\ | || 2/b l\ | || tan |- + -| | || tan |- - -| | \\ \2 2/ / \\ \2 2/ /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
2/b pi l\ 2/b l pi\
cos |- - -- - -| cos |- + - - --|
\2 2 2/ \2 2 2 /
1 - ---------------- 1 - ----------------
2/b l\ 2/b l\
cos |- - -| cos |- + -|
\2 2/ \2 2/
-------------------- - --------------------
2/b pi l\ 2/b l pi\
cos |- - -- - -| cos |- + - - --|
\2 2 2/ \2 2 2 /
1 + ---------------- 1 + ----------------
2/b l\ 2/b l\
cos |- - -| cos |- + -|
\2 2/ \2 2/
$$\frac{1 - \frac{\cos^{2}{\left(\frac{b}{2} - \frac{l}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{b}{2} - \frac{l}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}} - \frac{1 - \frac{\cos^{2}{\left(\frac{b}{2} + \frac{l}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{b}{2} + \frac{l}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}$$
2/b l\ 2/b l\
sec |- - -| sec |- + -|
\2 2/ \2 2/
1 - ---------------- 1 - ----------------
2/b pi l\ 2/b l pi\
sec |- - -- - -| sec |- + - - --|
\2 2 2/ \2 2 2 /
-------------------- - --------------------
2/b l\ 2/b l\
sec |- - -| sec |- + -|
\2 2/ \2 2/
1 + ---------------- 1 + ----------------
2/b pi l\ 2/b l pi\
sec |- - -- - -| sec |- + - - --|
\2 2 2/ \2 2 2 /
$$\frac{- \frac{\sec^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} - \frac{l}{2} - \frac{\pi}{2} \right)}} + 1}{\frac{\sec^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} - \frac{l}{2} - \frac{\pi}{2} \right)}} + 1} - \frac{- \frac{\sec^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} + \frac{l}{2} - \frac{\pi}{2} \right)}} + 1}{\frac{\sec^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} + \frac{l}{2} - \frac{\pi}{2} \right)}} + 1}$$
2/pi l b\ 2/pi b l\
csc |-- + - - -| csc |-- - - - -|
\2 2 2/ \2 2 2/
1 - ---------------- 1 - ----------------
2/b l\ 2/b l\
csc |- - -| csc |- + -|
\2 2/ \2 2/
-------------------- - --------------------
2/pi l b\ 2/pi b l\
csc |-- + - - -| csc |-- - - - -|
\2 2 2/ \2 2 2/
1 + ---------------- 1 + ----------------
2/b l\ 2/b l\
csc |- - -| csc |- + -|
\2 2/ \2 2/
$$\frac{1 - \frac{\csc^{2}{\left(- \frac{b}{2} + \frac{l}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}}{1 + \frac{\csc^{2}{\left(- \frac{b}{2} + \frac{l}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}} - \frac{1 - \frac{\csc^{2}{\left(- \frac{b}{2} - \frac{l}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}{1 + \frac{\csc^{2}{\left(- \frac{b}{2} - \frac{l}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}$$
// / pi\ \ // / pi \ \ || 0 for |b + l + --| mod pi = 0| || 0 for |b + -- - l| mod pi = 0| || \ 2 / | || \ 2 / | || | || | || /b l pi\ | || /b l pi\ | - |< 2*cot|- + - + --| | + |< 2*cot|- - - + --| | || \2 2 4 / | || \2 2 4 / | ||-------------------- otherwise | ||-------------------- otherwise | || 2/b l pi\ | || 2/b l pi\ | ||1 + cot |- + - + --| | ||1 + cot |- - - + --| | \\ \2 2 4 / / \\ \2 2 4 / /
$$\left(\begin{cases} 0 & \text{for}\: \left(b - l + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{b}{2} - \frac{l}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 0 & \text{for}\: \left(b + l + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// b \ // l \ // b \ // l \ || 0 for - mod pi = 0| || 0 for - mod pi = 0| || 1 for - mod 2*pi = 0| || 1 for - mod 2*pi = 0| || 2 | || 2 | || 2 | || 2 | 8*|< |*|< |*|< |*|< | || /b\ | || /l\ | || /b\ | || /l\ | ||sin|-| otherwise | ||sin|-| otherwise | ||cos|-| otherwise | ||cos|-| otherwise | \\ \2/ / \\ \2/ / \\ \2/ / \\ \2/ /
$$8 \left(\begin{cases} 0 & \text{for}\: \frac{b}{2} \bmod \pi = 0 \\\sin{\left(\frac{b}{2} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \frac{l}{2} \bmod \pi = 0 \\\sin{\left(\frac{l}{2} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \frac{b}{2} \bmod 2 \pi = 0 \\\cos{\left(\frac{b}{2} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \frac{l}{2} \bmod 2 \pi = 0 \\\cos{\left(\frac{l}{2} \right)} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ || | || 2 | || sin (b + l) | // 1 for (b - l) mod 2*pi = 0\ ||-1 + ------------- | || | || 4/b + l\ | || 2 4/b l\ | || 4*sin |-----| | ||sin (b - l) - 4*sin |- - -| | - |< \ 2 / | + |< \2 2/ | ||------------------ otherwise | ||--------------------------- otherwise | || 2 | || 2 4/b l\ | || sin (b + l) | ||sin (b - l) + 4*sin |- - -| | ||1 + ------------- | \\ \2 2/ / || 4/b + l\ | || 4*sin |-----| | \\ \ 2 / /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{- 4 \sin^{4}{\left(\frac{b}{2} - \frac{l}{2} \right)} + \sin^{2}{\left(b - l \right)}}{4 \sin^{4}{\left(\frac{b}{2} - \frac{l}{2} \right)} + \sin^{2}{\left(b - l \right)}} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(b + l \right)}}{4 \sin^{4}{\left(\frac{b + l}{2} \right)}}}{1 + \frac{\sin^{2}{\left(b + l \right)}}{4 \sin^{4}{\left(\frac{b + l}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | || 2 | || 2 | || sin (b + l) | || sin (b - l) | ||-1 + ------------- | ||-1 + ------------- | || 4/b l\ | || 4/b l\ | || 4*sin |- + -| | || 4*sin |- - -| | - |< \2 2/ | + |< \2 2/ | ||------------------ otherwise | ||------------------ otherwise | || 2 | || 2 | || sin (b + l) | || sin (b - l) | ||1 + ------------- | ||1 + ------------- | || 4/b l\ | || 4/b l\ | || 4*sin |- + -| | || 4*sin |- - -| | \\ \2 2/ / \\ \2 2/ /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(b - l \right)}}{4 \sin^{4}{\left(\frac{b}{2} - \frac{l}{2} \right)}}}{1 + \frac{\sin^{2}{\left(b - l \right)}}{4 \sin^{4}{\left(\frac{b}{2} - \frac{l}{2} \right)}}} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(b + l \right)}}{4 \sin^{4}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}{1 + \frac{\sin^{2}{\left(b + l \right)}}{4 \sin^{4}{\left(\frac{b}{2} + \frac{l}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | ||/ 1 for (b + l) mod 2*pi = 0 | ||/ 1 for (b - l) mod 2*pi = 0 | ||| | ||| | ||| 2/b l\ | ||| 2/b l\ | - |<|-1 + cot |- + -| | + |<|-1 + cot |- - -| | ||< \2 2/ otherwise | ||< \2 2/ otherwise | |||---------------- otherwise | |||---------------- otherwise | ||| 2/b l\ | ||| 2/b l\ | |||1 + cot |- + -| | |||1 + cot |- - -| | \\\ \2 2/ / \\\ \2 2/ /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} - 1}{\cot^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | || 2/b l\ | || 2/b l\ | || cos |- + -| | || cos |- - -| | || \2 2/ | || \2 2/ | ||-1 + ---------------- | ||-1 + ---------------- | || 2/b l pi\ | || 2/b pi l\ | || cos |- + - - --| | || cos |- - -- - -| | - |< \2 2 2 / | + |< \2 2 2/ | ||--------------------- otherwise | ||--------------------- otherwise | || 2/b l\ | || 2/b l\ | || cos |- + -| | || cos |- - -| | || \2 2/ | || \2 2/ | || 1 + ---------------- | || 1 + ---------------- | || 2/b l pi\ | || 2/b pi l\ | || cos |- + - - --| | || cos |- - -- - -| | \\ \2 2 2 / / \\ \2 2 2/ /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} - \frac{l}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} - \frac{l}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} + \frac{l}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} + \frac{l}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | || 2/b l pi\ | || 2/b pi l\ | || sec |- + - - --| | || sec |- - -- - -| | || \2 2 2 / | || \2 2 2/ | ||-1 + ---------------- | ||-1 + ---------------- | || 2/b l\ | || 2/b l\ | || sec |- + -| | || sec |- - -| | - |< \2 2/ | + |< \2 2/ | ||--------------------- otherwise | ||--------------------- otherwise | || 2/b l pi\ | || 2/b pi l\ | || sec |- + - - --| | || sec |- - -- - -| | || \2 2 2 / | || \2 2 2/ | || 1 + ---------------- | || 1 + ---------------- | || 2/b l\ | || 2/b l\ | || sec |- + -| | || sec |- - -| | \\ \2 2/ / \\ \2 2/ /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{b}{2} - \frac{l}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{b}{2} - \frac{l}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{b}{2} + \frac{l}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{b}{2} + \frac{l}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// b \ // l \ // b \ // l \ || 0 for - mod pi = 0| || 0 for - mod pi = 0| || 1 for - mod 2*pi = 0| || 1 for - mod 2*pi = 0| || 2 | || 2 | || 2 | || 2 | || | || | || | || | || /b\ | || /l\ | || 2/b\ | || 2/l\ | 8*|< 2*cot|-| |*|< 2*cot|-| |*|<-1 + cot |-| |*|<-1 + cot |-| | || \4/ | || \4/ | || \4/ | || \4/ | ||----------- otherwise | ||----------- otherwise | ||------------ otherwise | ||------------ otherwise | || 2/b\ | || 2/l\ | || 2/b\ | || 2/l\ | ||1 + cot |-| | ||1 + cot |-| | ||1 + cot |-| | ||1 + cot |-| | \\ \4/ / \\ \4/ / \\ \4/ / \\ \4/ /
$$8 \left(\begin{cases} 0 & \text{for}\: \frac{b}{2} \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{b}{4} \right)}}{\cot^{2}{\left(\frac{b}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \frac{l}{2} \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{l}{4} \right)}}{\cot^{2}{\left(\frac{l}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \frac{b}{2} \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{b}{4} \right)} - 1}{\cot^{2}{\left(\frac{b}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \frac{l}{2} \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{l}{4} \right)} - 1}{\cot^{2}{\left(\frac{l}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 1 for (b + l) mod 2*pi = 0\ // 1 for (b - l) mod 2*pi = 0\ || | || | || 2/b l\ | || 2/b l\ | || csc |- + -| | || csc |- - -| | || \2 2/ | || \2 2/ | ||-1 + ---------------- | ||-1 + ---------------- | || 2/pi b l\ | || 2/pi l b\ | || csc |-- - - - -| | || csc |-- + - - -| | - |< \2 2 2/ | + |< \2 2 2/ | ||--------------------- otherwise | ||--------------------- otherwise | || 2/b l\ | || 2/b l\ | || csc |- + -| | || csc |- - -| | || \2 2/ | || \2 2/ | || 1 + ---------------- | || 1 + ---------------- | || 2/pi b l\ | || 2/pi l b\ | || csc |-- - - - -| | || csc |-- + - - -| | \\ \2 2 2/ / \\ \2 2 2/ /
$$\left(\begin{cases} 1 & \text{for}\: \left(b - l\right) \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}{\csc^{2}{\left(- \frac{b}{2} + \frac{l}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{b}{2} - \frac{l}{2} \right)}}{\csc^{2}{\left(- \frac{b}{2} + \frac{l}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) - \left(\begin{cases} 1 & \text{for}\: \left(b + l\right) \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}{\csc^{2}{\left(- \frac{b}{2} - \frac{l}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{b}{2} + \frac{l}{2} \right)}}{\csc^{2}{\left(- \frac{b}{2} - \frac{l}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
-Piecewise((1, Mod(b + l = 2*pi, 0)), ((-1 + csc(b/2 + l/2)^2/csc(pi/2 - b/2 - l/2)^2)/(1 + csc(b/2 + l/2)^2/csc(pi/2 - b/2 - l/2)^2), True)) + Piecewise((1, Mod(b - l = 2*pi, 0)), ((-1 + csc(b/2 - l/2)^2/csc(pi/2 + l/2 - b/2)^2)/(1 + csc(b/2 - l/2)^2/csc(pi/2 + l/2 - b/2)^2), True))
Рациональный знаменатель
[src]
-cos(b + l) + cos(b - l)
$$\cos{\left(b - l \right)} - \cos{\left(b + l \right)}$$
-cos(b + l) + cos(b - l)
Общий знаменатель
[src]
-cos(b + l) + cos(b - l)
$$\cos{\left(b - l \right)} - \cos{\left(b + l \right)}$$
-cos(b + l) + cos(b - l)
Комбинаторика
[src]
-cos(b + l) + cos(b - l)
$$\cos{\left(b - l \right)} - \cos{\left(b + l \right)}$$
-cos(b + l) + cos(b - l)
Степени
[src]
-cos(b + l) + cos(b - l)
$$\cos{\left(b - l \right)} - \cos{\left(b + l \right)}$$
I*(b - l) I*(l - b) I*(b + l) I*(-b - l)
e e e e
---------- + ---------- - ---------- - -----------
2 2 2 2
$$- \frac{e^{i \left(- b - l\right)}}{2} + \frac{e^{i \left(- b + l\right)}}{2} + \frac{e^{i \left(b - l\right)}}{2} - \frac{e^{i \left(b + l\right)}}{2}$$
exp(i*(b - l))/2 + exp(i*(l - b))/2 - exp(i*(b + l))/2 - exp(i*(-b - l))/2
Объединение рациональных выражений
[src]
-cos(b + l) + cos(b - l)
$$\cos{\left(b - l \right)} - \cos{\left(b + l \right)}$$
-cos(b + l) + cos(b - l)