Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- n^2*sqrt(n)+2*n*sqrt(n)+2*sqrt(n) если n=4
- (50.7724*a^3+909*a/4)*(0.1161*a^4+2541*a^2/100) если a=4
- (-27*n+2*n^2+57)/(5*n/2+67/10-24*n/5) если n=-1/4
- -2*(37*x/10-1)-6-(-1)*(12*x/5)+8*(7*x/10-2) если x=-1/3
- Разложить многочлен на множители:
- x^4-x^2
- 4*x^2-y^2
- 4*x-x^2/2
- a^2-2*a*b+b^2
- Общий знаменатель:
- 6*a*b/a+6*b*(a/6*b-6*b/a)
- 5*m-9/(m-2)-3-2*m/(2-m)
- (b^2+8*b+16)/b*(b/(b+4)^2+b/(16-b^2))+8/(b-4)
- (c+12)/(15*c)-(3*b-5)/(45*b)
- Умножение столбиком:
- 6699*89
- 570*845
- 6769*23
- 83*194
- Деление столбиком:
- 4078/2
- 4197/2
- 4212/2
- 4226/2
- Раскрыть скобки в:
- (7*a+2*b)^2-3*(a-b)*(4*a+5*b)
- (3*x^5+5*x^4+13*x)*(x^2+x+5)
- -(3-4*m-2*m^2+4*m^3-m^4)^2-(3-4*m-2*m^2+4*m^3-m^4)+2*m*(3-4*m-2*m^2+4*m^3-m^4)-2*m+2
- 2*k*(4-3*k)+3*k-4
- Разложение числа на простые множители:
- 68623
- 56129
- 80643
- 32294
- Производная:
- 1/4
- Интеграл d{x}:
-
1/4
- График функции y =:
- 1/4
-
Идентичные выражения
- tan(сорок два *c)*tan(сорок два) если c= один / четыре
- тангенс от (42 умножить на c) умножить на тангенс от (42) если c равно 1 делить на 4
- тангенс от (сорок два умножить на c) умножить на тангенс от (сорок два) если c равно один делить на четыре
- tan(42c)tan(42) если c=1/4
- tan42ctan42 если c=1/4
- tan(42*c)*tan(42) при c=1/4
- tan(42*c)*tan(42) если c=1 разделить на 4
tan(42*c)*tan(42) если c=1/4
Решение
Вы ввели
[src]
tan(42*c)*tan(42)
$$\tan{\left(42 \right)} \tan{\left(42 c \right)}$$
tan(42*c)*tan(42)
Подстановка условия
[src]
tan(42*c)*tan(42) при c = 1/4
подставляем
tan(42*c)*tan(42)
$$\tan{\left(42 \right)} \tan{\left(42 c \right)}$$
tan(42)*tan(42*c)
$$\tan{\left(42 \right)} \tan{\left(42 c \right)}$$
переменные
c = 1/4
$$c = \frac{1}{4}$$
tan(42)*tan(42*(1/4))
$$\tan{\left(42 \right)} \tan{\left(42 (1/4) \right)}$$
tan(42)*tan(21/2)
$$\tan{\left(\frac{21}{2} \right)} \tan{\left(42 \right)}$$
tan(42)*tan(21/2)
Тригонометрическая часть
[src]
1 ----------------- cot(42)*cot(42*c)
$$\frac{1}{\cot{\left(42 \right)} \cot{\left(42 c \right)}}$$
sin(42)*sin(42*c) ----------------- cos(42)*cos(42*c)
$$\frac{\sin{\left(42 \right)} \sin{\left(42 c \right)}}{\cos{\left(42 \right)} \cos{\left(42 c \right)}}$$
sec(42)*sec(42*c) ----------------- csc(42)*csc(42*c)
$$\frac{\sec{\left(42 \right)} \sec{\left(42 c \right)}}{\csc{\left(42 \right)} \csc{\left(42 c \right)}}$$
2
4*sin (42)*csc(84)*csc(84*c)
----------------------------
2
csc (42*c)
$$\frac{4 \sin^{2}{\left(42 \right)} \csc{\left(84 \right)} \csc{\left(84 c \right)}}{\csc^{2}{\left(42 c \right)}}$$
4*csc(84)*csc(84*c) ------------------- 2 2 csc (42)*csc (42*c)
$$\frac{4 \csc{\left(84 \right)} \csc{\left(84 c \right)}}{\csc^{2}{\left(42 \right)} \csc^{2}{\left(42 c \right)}}$$
2 2 4*sin (42)*sin (42*c) --------------------- sin(84)*sin(84*c)
$$\frac{4 \sin^{2}{\left(42 \right)} \sin^{2}{\left(42 c \right)}}{\sin{\left(84 \right)} \sin{\left(84 c \right)}}$$
sin(42)*sin(42*c) --------------------------- / pi\ /pi \ sin|42 + --|*sin|-- + 42*c| \ 2 / \2 /
$$\frac{\sin{\left(42 \right)} \sin{\left(42 c \right)}}{\sin{\left(\frac{\pi}{2} + 42 \right)} \sin{\left(42 c + \frac{\pi}{2} \right)}}$$
sec(42)*sec(42*c) --------------------------- / pi\ / pi\ sec|42 - --|*sec|42*c - --| \ 2 / \ 2 /
$$\frac{\sec{\left(42 \right)} \sec{\left(42 c \right)}}{\sec{\left(- \frac{\pi}{2} + 42 \right)} \sec{\left(42 c - \frac{\pi}{2} \right)}}$$
/ pi\ / pi\
cos|42 - --|*cos|42*c - --|
\ 2 / \ 2 /
---------------------------
cos(42)*cos(42*c)
$$\frac{\cos{\left(- \frac{\pi}{2} + 42 \right)} \cos{\left(42 c - \frac{\pi}{2} \right)}}{\cos{\left(42 \right)} \cos{\left(42 c \right)}}$$
sec(42)*sec(42*c) ---------------------------- / pi\ /pi \ sec|-42 + --|*sec|-- - 42*c| \ 2 / \2 /
$$\frac{\sec{\left(42 \right)} \sec{\left(42 c \right)}}{\sec{\left(-42 + \frac{\pi}{2} \right)} \sec{\left(- 42 c + \frac{\pi}{2} \right)}}$$
/ pi\ /pi \
csc|-42 + --|*csc|-- - 42*c|
\ 2 / \2 /
----------------------------
csc(42)*csc(42*c)
$$\frac{\csc{\left(-42 + \frac{\pi}{2} \right)} \csc{\left(- 42 c + \frac{\pi}{2} \right)}}{\csc{\left(42 \right)} \csc{\left(42 c \right)}}$$
4*tan(21)*tan(21*c) ------------------------------- / 2 \ / 2 \ \1 - tan (21)/*\1 - tan (21*c)/
$$\frac{4 \tan{\left(21 \right)} \tan{\left(21 c \right)}}{\left(- \tan^{2}{\left(21 \right)} + 1\right) \left(- \tan^{2}{\left(21 c \right)} + 1\right)}$$
/ pi\ /pi \ csc|-42 + --|*csc|-- - 42*c| \ 2 / \2 / ---------------------------- csc(-42 + pi)*csc(pi - 42*c)
$$\frac{\csc{\left(-42 + \frac{\pi}{2} \right)} \csc{\left(- 42 c + \frac{\pi}{2} \right)}}{\csc{\left(-42 + \pi \right)} \csc{\left(- 42 c + \pi \right)}}$$
-cos(42*(1 + c)) + cos(42*(-1 + c)) ----------------------------------- cos(42*(1 + c)) + cos(42*(-1 + c))
$$\frac{\cos{\left(42 \left(c - 1\right) \right)} - \cos{\left(42 \left(c + 1\right) \right)}}{\cos{\left(42 \left(c - 1\right) \right)} + \cos{\left(42 \left(c + 1\right) \right)}}$$
/ pi\ / pi\
4*sec|84 - --|*sec|84*c - --|
\ 2 / \ 2 /
-----------------------------
2/ pi\ 2/ pi\
sec |42 - --|*sec |42*c - --|
\ 2 / \ 2 /
$$\frac{4 \sec{\left(- \frac{\pi}{2} + 84 \right)} \sec{\left(84 c - \frac{\pi}{2} \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + 42 \right)} \sec^{2}{\left(42 c - \frac{\pi}{2} \right)}}$$
2/ pi\ 2/ pi\
4*cos |42 - --|*cos |42*c - --|
\ 2 / \ 2 /
-------------------------------
/ pi\ / pi\
cos|84 - --|*cos|84*c - --|
\ 2 / \ 2 /
$$\frac{4 \cos^{2}{\left(- \frac{\pi}{2} + 42 \right)} \cos^{2}{\left(42 c - \frac{\pi}{2} \right)}}{\cos{\left(- \frac{\pi}{2} + 84 \right)} \cos{\left(84 c - \frac{\pi}{2} \right)}}$$
2 2 / 1 \
-8*cos (21)*sin (21)*|------- + tan(42)|*cos(21*c)*sin(21*c)
\tan(42) /
------------------------------------------------------------
2
-1 + 2*sin (21*c)
$$- \frac{8 \cdot \left(\frac{1}{\tan{\left(42 \right)}} + \tan{\left(42 \right)}\right) \sin^{2}{\left(21 \right)} \sin{\left(21 c \right)} \cos^{2}{\left(21 \right)} \cos{\left(21 c \right)}}{2 \sin^{2}{\left(21 c \right)} - 1}$$
2 2
4*cos (21)*cos (21*c)*tan(21)*tan(21*c)
-----------------------------------------------------
2 2 2 2
1 - 2*cos (21) - 2*cos (21*c) + 4*cos (21)*cos (21*c)
$$\frac{4 \cos^{2}{\left(21 \right)} \cos^{2}{\left(21 c \right)} \tan{\left(21 \right)} \tan{\left(21 c \right)}}{- 2 \cos^{2}{\left(21 c \right)} + 4 \cos^{2}{\left(21 \right)} \cos^{2}{\left(21 c \right)} - 2 \cos^{2}{\left(21 \right)} + 1}$$
// 0 for 42*c mod pi = 0\ // zoo for 84*c mod pi = 0\ || | || | 2*|<1 - cos(84*c) |*|< 1 |*tan(42) ||------------- otherwise | ||--------- otherwise | \\ 2 / \\sin(84*c) /
$$2 \left(\begin{cases} 0 & \text{for}\: 42 c \bmod \pi = 0 \\\frac{- \cos{\left(84 c \right)} + 1}{2} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: 84 c \bmod \pi = 0 \\\frac{1}{\sin{\left(84 c \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(42 \right)}$$
2 2 / 2 \ / 2 \
16*tan (21)*tan (21*c)*\1 + tan (42)/*\1 + tan (42*c)/
------------------------------------------------------
2 2
/ 2 \ / 2 \
\1 + tan (21)/ *\1 + tan (21*c)/ *tan(42)*tan(42*c)
$$\frac{16 \cdot \left(1 + \tan^{2}{\left(42 \right)}\right) \left(\tan^{2}{\left(42 c \right)} + 1\right) \tan^{2}{\left(21 \right)} \tan^{2}{\left(21 c \right)}}{\left(1 + \tan^{2}{\left(21 \right)}\right)^{2} \left(\tan^{2}{\left(21 c \right)} + 1\right)^{2} \tan{\left(42 \right)} \tan{\left(42 c \right)}}$$
/ 2/ pi\\ / 2/ pi\\
|1 + tan |21 + --||*|1 + tan |21*c + --||*cot(21)*cot(21*c)
\ \ 4 // \ \ 4 //
-----------------------------------------------------------
/ 2 \ / 2 \ / pi\ / pi\
\1 + cot (21)/*\1 + cot (21*c)/*tan|21 + --|*tan|21*c + --|
\ 4 / \ 4 /
$$\frac{\left(\tan^{2}{\left(\frac{\pi}{4} + 21 \right)} + 1\right) \left(\tan^{2}{\left(21 c + \frac{\pi}{4} \right)} + 1\right) \cot{\left(21 \right)} \cot{\left(21 c \right)}}{\left(\cot^{2}{\left(21 \right)} + 1\right) \left(\cot^{2}{\left(21 c \right)} + 1\right) \tan{\left(\frac{\pi}{4} + 21 \right)} \tan{\left(21 c + \frac{\pi}{4} \right)}}$$
/ 2/ pi\\ / 2/ pi\\
|1 - cot |21 + --||*|1 - cot |21*c + --||*(1 + sin(42))*(1 + sin(42*c))
\ \ 4 // \ \ 4 //
-----------------------------------------------------------------------
/ 2 \ / 2 \ 2 2
4*\1 - tan (21)/*\1 - tan (21*c)/*cos (21)*cos (21*c)
$$\frac{\left(- \cot^{2}{\left(\frac{\pi}{4} + 21 \right)} + 1\right) \left(- \cot^{2}{\left(21 c + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(42 \right)} + 1\right) \left(\sin{\left(42 c \right)} + 1\right)}{4 \cdot \left(- \tan^{2}{\left(21 \right)} + 1\right) \left(- \tan^{2}{\left(21 c \right)} + 1\right) \cos^{2}{\left(21 \right)} \cos^{2}{\left(21 c \right)}}$$
// 1 for 21*c mod pi = 0\ // / 3*pi\ \
2 || | || 1 for |42*c + ----| mod 2*pi = 0|
-4*tan (21)*|< 1 |*|< \ 2 / |
||--------- otherwise | || |
\\cos(42*c) / \\sin(42*c) otherwise /
------------------------------------------------------------------------------------------
/ 4 \
\-1 + tan (21)/*sin(42)
$$- \frac{4 \left(\begin{cases} 1 & \text{for}\: 21 c \bmod \pi = 0 \\\frac{1}{\cos{\left(42 c \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(42 c + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(42 c \right)} & \text{otherwise} \end{cases}\right) \tan^{2}{\left(21 \right)}}{\left(-1 + \tan^{4}{\left(21 \right)}\right) \sin{\left(42 \right)}}$$
/ 2 \ / 2 \ / 2/ pi\\ / 2/ pi\\
\1 + cot (21)/*\1 + cot (21*c)/*|-1 + tan |21 + --||*|-1 + tan |21*c + --||
\ \ 4 // \ \ 4 //
---------------------------------------------------------------------------
/ 2/ pi\\ / 2/ pi\\ / 2 \ / 2 \
|1 + tan |21 + --||*|1 + tan |21*c + --||*\-1 + cot (21)/*\-1 + cot (21*c)/
\ \ 4 // \ \ 4 //
$$\frac{\left(-1 + \tan^{2}{\left(\frac{\pi}{4} + 21 \right)}\right) \left(\tan^{2}{\left(21 c + \frac{\pi}{4} \right)} - 1\right) \left(\cot^{2}{\left(21 \right)} + 1\right) \left(\cot^{2}{\left(21 c \right)} + 1\right)}{\left(-1 + \cot^{2}{\left(21 \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{4} + 21 \right)} + 1\right) \left(\tan^{2}{\left(21 c + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(21 c \right)} - 1\right)}$$
/ 2 \ / 2 \ / 2/ pi\\ / 2/ pi\\
\1 + tan (21)/*\1 + tan (21*c)/*|1 - cot |21 + --||*|1 - cot |21*c + --||
\ \ 4 // \ \ 4 //
-------------------------------------------------------------------------
/ 2/ pi\\ / 2/ pi\\ / 2 \ / 2 \
|1 + cot |21 + --||*|1 + cot |21*c + --||*\1 - tan (21)/*\1 - tan (21*c)/
\ \ 4 // \ \ 4 //
$$\frac{\left(1 + \tan^{2}{\left(21 \right)}\right) \left(- \cot^{2}{\left(\frac{\pi}{4} + 21 \right)} + 1\right) \left(- \cot^{2}{\left(21 c + \frac{\pi}{4} \right)} + 1\right) \left(\tan^{2}{\left(21 c \right)} + 1\right)}{\left(- \tan^{2}{\left(21 \right)} + 1\right) \left(- \tan^{2}{\left(21 c \right)} + 1\right) \left(1 + \cot^{2}{\left(\frac{\pi}{4} + 21 \right)}\right) \left(\cot^{2}{\left(21 c + \frac{\pi}{4} \right)} + 1\right)}$$
// 0 for 42*c mod pi = 0\
|| | // zoo for 84*c mod pi = 0\
|| 2 | || |
2 / 2 \ || 4*cot (21*c) | || 2 |
8*cot (21)*\1 + cot (42)/*|<----------------- otherwise |*|<1 + cot (42*c) |
|| 2 | ||-------------- otherwise |
||/ 2 \ | || 2*cot(42*c) |
||\1 + cot (21*c)/ | \\ /
\\ /
----------------------------------------------------------------------------------------------------------
2
/ 2 \
\1 + cot (21)/ *cot(42)
$$\frac{8 \left(\cot^{2}{\left(42 \right)} + 1\right) \left(\begin{cases} 0 & \text{for}\: 42 c \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(21 c \right)}}{\left(\cot^{2}{\left(21 c \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: 84 c \bmod \pi = 0 \\\frac{\cot^{2}{\left(42 c \right)} + 1}{2 \cot{\left(42 c \right)}} & \text{otherwise} \end{cases}\right) \cot^{2}{\left(21 \right)}}{\left(\cot^{2}{\left(21 \right)} + 1\right)^{2} \cot{\left(42 \right)}}$$
// / 3*pi\ \
|| 1 for |42*c + ----| mod 2*pi = 0|
// 1 for 21*c mod pi = 0\ || \ 2 / |
|| | || |
/ 2 \ / 2/ pi\\ || 2 | || 2/ pi\ |
\1 + cot (21)/*|-1 + tan |21 + --||*|< 1 + cot (21*c) |*|<-1 + tan |21*c + --| |
\ \ 4 // ||--------------- otherwise | || \ 4 / |
|| 2 | ||-------------------- otherwise |
\\-1 + cot (21*c) / || 2/ pi\ |
||1 + tan |21*c + --| |
\\ \ 4 / /
-----------------------------------------------------------------------------------------------------------------------------------
/ 2/ pi\\ / 2 \
|1 + tan |21 + --||*\-1 + cot (21)/
\ \ 4 //
$$\frac{\left(-1 + \tan^{2}{\left(\frac{\pi}{4} + 21 \right)}\right) \left(\cot^{2}{\left(21 \right)} + 1\right) \left(\begin{cases} 1 & \text{for}\: 21 c \bmod \pi = 0 \\\frac{\cot^{2}{\left(21 c \right)} + 1}{\cot^{2}{\left(21 c \right)} - 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(42 c + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(21 c + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(21 c + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)}{\left(-1 + \cot^{2}{\left(21 \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{4} + 21 \right)} + 1\right)}$$
(1 + cot(21)^2)*(-1 + tan(21 + pi/4)^2)*Piecewise((1, Mod(21*c = pi, 0)), ((1 + cot(21*c)^2)/(-1 + cot(21*c)^2), True))*Piecewise((1, Mod(42*c + 3*pi/2 = 2*pi, 0)), ((-1 + tan(21*c + pi/4)^2)/(1 + tan(21*c + pi/4)^2), True))/((1 + tan(21 + pi/4)^2)*(-1 + cot(21)^2))
Степени
[src]
/ 42*I -42*I\ / 42*I*c -42*I*c\ -\- e + e /*\- e + e / ------------------------------------------- / -42*I 42*I\ / -42*I*c 42*I*c\ \e + e /*\e + e /
$$- \frac{\left(e^{- 42 i} - e^{42 i}\right) \left(- e^{42 i c} + e^{- 42 i c}\right)}{\left(e^{42 i} + e^{- 42 i}\right) \left(e^{42 i c} + e^{- 42 i c}\right)}$$
-(-exp(42*i) + exp(-42*i))*(-exp(42*i*c) + exp(-42*i*c))/((exp(-42*i) + exp(42*i))*(exp(-42*i*c) + exp(42*i*c)))