Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- 1/x-(1/x-11/(5*x+1000000))/(1+10/(15+1000*x)+10/(5+1000000/x)) если x=-3/2
- (x^5-4*x^4-9*x^3+32*x^2+28*x-48)*(x^4+2*x^3-13*x^2-38*x-24) если x=4
- x^2-4 если x=-3
- c*35*8 если c=-1/4
- Разложить многочлен на множители:
- x^2-64*z^2
- 4*x^2+16*y^2
- 3*x^2-2*x-16
- x^3-4*x^2+3*x
- Общий знаменатель:
- (4*p-q)/(12*p^2*q)+(p-5*q)/(15*p*q^2)
- 2*(log(sin(x)/(1+cos(x))+1)/4-log((3*sin(x))/(1+cos(x))-1)/4)
- 3*((x^3*asin(x))/3-((-(x^2*sqrt(1-x^2))/3)-(2*sqrt(1-x^2))/3)/3)
- (i*j*(2*k-1))/((i/n1)*(j/n2)*((2*k/n3)-1))
- Умножение столбиком:
- 822*719
- 1915*39
- 5926*13
- 37*821
- Деление столбиком:
- 9904/2
- 10882/2
- 11264/2
- 11302/2
- Раскрыть скобки в:
- (3*x-2)^2-3*x^2+(7*x-3)^2-x^2*(27*x-7)+6*x
- 3*x^2*(x-1)^2-(x^3-2*x^2)*(2*x-2)
- (33-17)*(42345-32306)
- (x^2+4*x+4)*(x^2-5*x)
- Разложение числа на простые множители:
- 23752
- 61748
- 66136
- 16890
- График функции y =:
- -1
- Производная:
- -1
- Интеграл d{x}:
-
-1
-
Идентичные выражения
- tan(a)+cot(a) если a=- один
- тангенс от (a) плюс котангенс от (a) если a равно минус 1
- тангенс от (a) плюс котангенс от (a) если a равно минус один
- tana+cota если a=-1
- tan(a)+cot(a) при a=-1
-
Похожие выражения
- tan(a)-cot(a) если a=-1
- tan(a)+cot(a) если a=+1
tan(a)+cot(a) если a=-1
Решение
Подстановка условия
[src]
tan(a) + cot(a) при a = -1
подставляем
tan(a) + cot(a)
$$\tan{\left(a \right)} + \cot{\left(a \right)}$$
cot(a) + tan(a)
$$\tan{\left(a \right)} + \cot{\left(a \right)}$$
переменные
a = -1
$$a = -1$$
cot((-1)) + tan((-1))
$$\tan{\left((-1) \right)} + \cot{\left((-1) \right)}$$
cot(-1) + tan(-1)
$$\tan{\left(-1 \right)} + \cot{\left(-1 \right)}$$
-cot(1) - tan(1)
$$- \tan{\left(1 \right)} - \cot{\left(1 \right)}$$
-cot(1) - tan(1)
Степени
[src]
/ I*a -I*a\
I*\- e + e /
------------------ + cot(a)
I*a -I*a
e + e
$$\cot{\left(a \right)} + \frac{i \left(- e^{i a} + e^{- i a}\right)}{e^{i a} + e^{- i a}}$$
i*(-exp(i*a) + exp(-i*a))/(exp(i*a) + exp(-i*a)) + cot(a)
Тригонометрическая часть
[src]
1 ------ + tan(a) tan(a)
$$\tan{\left(a \right)} + \frac{1}{\tan{\left(a \right)}}$$
1 ------ + cot(a) cot(a)
$$\cot{\left(a \right)} + \frac{1}{\cot{\left(a \right)}}$$
sec(a) csc(a) ------ + ------ csc(a) sec(a)
$$\frac{\csc{\left(a \right)}}{\sec{\left(a \right)}} + \frac{\sec{\left(a \right)}}{\csc{\left(a \right)}}$$
sin(a) cos(a) ------ + ------ cos(a) sin(a)
$$\frac{\sin{\left(a \right)}}{\cos{\left(a \right)}} + \frac{\cos{\left(a \right)}}{\sin{\left(a \right)}}$$
1 /a\
------ - tan|-|
/a\ \2/
tan|-|
\2/
--------------- + tan(a)
2
$$\frac{- \tan{\left(\frac{a}{2} \right)} + \frac{1}{\tan{\left(\frac{a}{2} \right)}}}{2} + \tan{\left(a \right)}$$
/a\
tan|-|
1 \2/
-------- - ------ + tan(a)
/a\ 2
2*tan|-|
\2/
$$- \frac{\tan{\left(\frac{a}{2} \right)}}{2} + \tan{\left(a \right)} + \frac{1}{2 \tan{\left(\frac{a}{2} \right)}}$$
2
sin(2*a) 2*sin (a)
--------- + ---------
2 sin(2*a)
2*sin (a)
$$\frac{2 \sin^{2}{\left(a \right)}}{\sin{\left(2 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}}$$
2
csc (a) 2*csc(2*a)
---------- + ----------
2*csc(2*a) 2
csc (a)
$$\frac{\csc^{2}{\left(a \right)}}{2 \csc{\left(2 a \right)}} + \frac{2 \csc{\left(2 a \right)}}{\csc^{2}{\left(a \right)}}$$
/ pi\
cos|a - --|
\ 2 / cos(a)
----------- + -----------
cos(a) / pi\
cos|a - --|
\ 2 /
$$\frac{\cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + \frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(a \right)}}$$
/ pi\
sec|a - --|
\ 2 / sec(a)
----------- + -----------
sec(a) / pi\
sec|a - --|
\ 2 /
$$\frac{\sec{\left(a \right)}}{\sec{\left(a - \frac{\pi}{2} \right)}} + \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}$$
/ pi\
sin|a + --|
\ 2 / sin(a)
----------- + -----------
sin(a) / pi\
sin|a + --|
\ 2 /
$$\frac{\sin{\left(a \right)}}{\sin{\left(a + \frac{\pi}{2} \right)}} + \frac{\sin{\left(a + \frac{\pi}{2} \right)}}{\sin{\left(a \right)}}$$
/pi \
sec|-- - a|
\2 / sec(a)
----------- + -----------
sec(a) /pi \
sec|-- - a|
\2 /
$$\frac{\sec{\left(a \right)}}{\sec{\left(- a + \frac{\pi}{2} \right)}} + \frac{\sec{\left(- a + \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}$$
/pi \
csc|-- - a|
\2 / csc(a)
----------- + -----------
csc(a) /pi \
csc|-- - a|
\2 /
$$\frac{\csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- a + \frac{\pi}{2} \right)}}{\csc{\left(a \right)}}$$
/pi \
csc|-- - a|
\2 / csc(pi - a)
----------- + -----------
csc(pi - a) /pi \
csc|-- - a|
\2 /
$$\frac{\csc{\left(- a + \pi \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- a + \frac{\pi}{2} \right)}}{\csc{\left(- a + \pi \right)}}$$
2/a\ /a\
1 - tan |-| 2*tan|-|
\2/ \2/
----------- + -----------
/a\ 2/a\
2*tan|-| 1 - tan |-|
\2/ \2/
$$\frac{- \tan^{2}{\left(\frac{a}{2} \right)} + 1}{2 \tan{\left(\frac{a}{2} \right)}} + \frac{2 \tan{\left(\frac{a}{2} \right)}}{- \tan^{2}{\left(\frac{a}{2} \right)} + 1}$$
/ pi\ 2/ pi\
cos|2*a - --| 2*cos |a - --|
\ 2 / \ 2 /
-------------- + --------------
2/ pi\ / pi\
2*cos |a - --| cos|2*a - --|
\ 2 / \ 2 /
$$\frac{2 \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(2 a - \frac{\pi}{2} \right)}} + \frac{\cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos^{2}{\left(a - \frac{\pi}{2} \right)}}$$
2/ pi\ / pi\
sec |a - --| 2*sec|2*a - --|
\ 2 / \ 2 /
--------------- + ---------------
/ pi\ 2/ pi\
2*sec|2*a - --| sec |a - --|
\ 2 / \ 2 /
$$\frac{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}{2 \sec{\left(2 a - \frac{\pi}{2} \right)}} + \frac{2 \sec{\left(2 a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$
2/a\
-1 + 2*cos |-|
\2/ sin(a)
-------------- - ----------------------
sin(a) / 1 \ 2/a\
|-2 + -------|*cos |-|
| 2/a\| \2/
| cos |-||
\ \2//
$$\frac{2 \cos^{2}{\left(\frac{a}{2} \right)} - 1}{\sin{\left(a \right)}} - \frac{\sin{\left(a \right)}}{\left(-2 + \frac{1}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos^{2}{\left(\frac{a}{2} \right)}}$$
1 /a\
------ - tan|-|
/a\ \2/ / 2/a pi\\
tan|-| |1 - cot |- + --||*(1 + sin(a))
\2/ \ \2 4 //
--------------- + -------------------------------
2 / 2/a\\ 2/a\
2*|1 - tan |-||*cos |-|
\ \2// \2/
$$\frac{- \tan{\left(\frac{a}{2} \right)} + \frac{1}{\tan{\left(\frac{a}{2} \right)}}}{2} + \frac{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(a \right)} + 1\right)}{2 \cdot \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \cos^{2}{\left(\frac{a}{2} \right)}}$$
2
2/a\ / 2 \ / 2/a\\
4*tan |-|*\1 + tan (a)/ |1 + tan |-|| *tan(a)
\2/ \ \2//
----------------------- + -----------------------
2 / 2 \ 2/a\
/ 2/a\\ 4*\1 + tan (a)/*tan |-|
|1 + tan |-|| *tan(a) \2/
\ \2//
$$\frac{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)}}{4 \left(\tan^{2}{\left(a \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)}} + \frac{4 \left(\tan^{2}{\left(a \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)}}$$
/ 2/a pi\\ /a\ / 2/a\\ /a pi\ |1 + tan |- + --||*cot|-| |1 + cot |-||*tan|- + --| \ \2 4 // \2/ \ \2// \2 4 / ------------------------- + ------------------------- / 2/a\\ /a pi\ / 2/a pi\\ /a\ |1 + cot |-||*tan|- + --| |1 + tan |- + --||*cot|-| \ \2// \2 4 / \ \2 4 // \2/
$$\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)}}$$
/ 2/a pi\\ / 2/a\\ / 2/a\\ / 2/a pi\\ |1 + tan |- + --||*|-1 + cot |-|| |1 + cot |-||*|-1 + tan |- + --|| \ \2 4 // \ \2// \ \2// \ \2 4 // --------------------------------- + --------------------------------- / 2/a\\ / 2/a pi\\ / 2/a pi\\ / 2/a\\ |1 + cot |-||*|-1 + tan |- + --|| |1 + tan |- + --||*|-1 + cot |-|| \ \2// \ \2 4 // \ \2 4 // \ \2//
$$\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)} + \frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)}$$
/ 2/a\\ / 2/a pi\\ / 2/a pi\\ / 2/a\\ |1 + tan |-||*|1 - cot |- + --|| |1 + cot |- + --||*|1 - tan |-|| \ \2// \ \2 4 // \ \2 4 // \ \2// -------------------------------- + -------------------------------- / 2/a pi\\ / 2/a\\ / 2/a\\ / 2/a pi\\ |1 + cot |- + --||*|1 - tan |-|| |1 + tan |-||*|1 - cot |- + --|| \ \2 4 // \ \2// \ \2// \ \2 4 //
$$\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)}{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)} + \frac{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)}{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)}$$
// zoo for a mod pi = 0\
|| |
// 0 for 2*a mod pi = 0\ || 1 |
|< |*|<------- otherwise |
\\sin(2*a) otherwise / || 2 |
||sin (a) | // 0 for a mod pi = 0\ // zoo for 2*a mod pi = 0\
\\ / || | || |
------------------------------------------------------------ + 2*|< 2 |*|< 1 |
2 ||sin (a) otherwise | ||-------- otherwise |
\\ / \\sin(2*a) /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: 2 a \bmod \pi = 0 \\\frac{1}{\sin{\left(2 a \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\sin{\left(2 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right)}{2}\right)$$
// / 3*pi\ \
|| 1 for |a + ----| mod 2*pi = 0|
|| \ 2 / |
// 1 for a mod 2*pi = 0\ // / 3*pi\ \ || |
|| | || 1 for |a + ----| mod 2*pi = 0| // 1 for a mod 2*pi = 0\ || 1 /a\ |
|< 1 |*|< \ 2 / | + |< |*|<------ + tan|-| |
||------ otherwise | || | \\cos(a) otherwise / || /a\ \2/ |
\\cos(a) / \\sin(a) otherwise / ||tan|-| |
|| \2/ |
||--------------- otherwise |
\\ 2 /
$$\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\cos{\left(a \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan{\left(\frac{a}{2} \right)} + \frac{1}{\tan{\left(\frac{a}{2} \right)}}}{2} & \text{otherwise} \end{cases}\right)\right)$$
// zoo for a mod pi = 0\
|| |
// 0 for 2*a mod pi = 0\ || 2 |
|| | ||/ 2/a\\ |
|| 2*cot(a) | |||1 + cot |-|| |
|<----------- otherwise |*|<\ \2// |
|| 2 | ||-------------- otherwise | // 0 for a mod pi = 0\
||1 + cot (a) | || 2/a\ | || |
\\ / || 4*cot |-| | || 2/a\ | // zoo for 2*a mod pi = 0\
|| \2/ | || 4*cot |-| | || |
\\ / || \2/ | || 2 |
---------------------------------------------------------------------- + 2*|<-------------- otherwise |*|<1 + cot (a) |
2 || 2 | ||----------- otherwise |
||/ 2/a\\ | || 2*cot(a) |
|||1 + cot |-|| | \\ /
||\ \2// |
\\ /
$$\left(2 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: 2 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(a \right)} + 1}{2 \cot{\left(a \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: a \bmod \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{4 \cot^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)}{2}\right)$$
// / 3*pi\ \ // / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0| // 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| | || \ 2 / | || | || \ 2 / |
|| 2/a\ | || | || 2/a\ | || |
||-1 + cot |-| | || 2/a pi\ | ||1 + cot |-| | || 2/a pi\ |
|< \2/ |*|< 1 + tan |- + --| | + |< \2/ |*|<-1 + tan |- + --| |
||------------ otherwise | || \2 4 / | ||------------ otherwise | || \2 4 / |
|| 2/a\ | ||----------------- otherwise | || 2/a\ | ||----------------- otherwise |
||1 + cot |-| | || 2/a pi\ | ||-1 + cot |-| | || 2/a pi\ |
\\ \2/ / ||-1 + tan |- + --| | \\ \2/ / || 1 + tan |- + --| |
\\ \2 4 / / \\ \2 4 / /
$$\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} \right)} + 1}{\cot^{2}{\left(\frac{a}{2} \right)} - 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1} & \text{otherwise} \end{cases}\right)\right)$$
Piecewise((1, Mod(a = 2*pi, 0)), ((-1 + cot(a/2)^2)/(1 + cot(a/2)^2), True))*Piecewise((1, Mod(a + 3*pi/2 = 2*pi, 0)), ((1 + tan(a/2 + pi/4)^2)/(-1 + tan(a/2 + pi/4)^2), True)) + Piecewise((1, Mod(a = 2*pi, 0)), ((1 + cot(a/2)^2)/(-1 + cot(a/2)^2), True))*Piecewise((1, Mod(a + 3*pi/2 = 2*pi, 0)), ((-1 + tan(a/2 + pi/4)^2)/(1 + tan(a/2 + pi/4)^2), True))