Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- x^2+5*x-14 если x=-2
- 1/(cos(t)^2)-1 если t=1/3
- sin(a-b)*cos(b)+cos(a-b)*sin(b) если a=1/2
- 9^(x^2-x-5)+6^(x^2-x-4)-180*4^(x^2-x+7) если x=-2
- Разложить многочлен на множители:
- x^3+64
- p-p^2
- b^3-8
- x^5-y^5
- Общий знаменатель:
- (8/(b^2-25))-(4/(b^2+5*b))
- (b^-1+8/(b^-2-14*b^-1+49))/(b^-2-64)/(7*b^-1-49)-7/b^-1-8
- 16*a^3/5*b-35*b^2/12*a^4
- 8*a-15/a-3*y-12/y
- Умножение столбиком:
- 14*50
- 48*15
- 40*12
- 17*30
- Деление столбиком:
- 87/9
- 24/6
- 637/5
- 136/3
- Раскрыть скобки в:
- (k+1)*(2*k+1)^2
- z*(-z)*(-z)^12
- 2*x*(-1)
- z*(-z)*(-z)^6
- Разложение числа на простые множители:
- 10850
- 45630
- 65
- 820
- Производная:
- 1/3
- График функции y =:
- 1/3
- Интеграл d{x}:
-
1/3
-
Идентичные выражения
- один /(cos(t)^ два)- один если t= один / три
- 1 делить на ( косинус от (t) в квадрате ) минус 1 если t равно 1 делить на 3
- один делить на ( косинус от (t) в степени два) минус один если t равно один делить на три
- 1/(cos(t)2)-1 если t=1/3
- 1/cost2-1 если t=1/3
- 1/(cos(t)²)-1 если t=1/3
- 1/(cos(t) в степени 2)-1 если t=1/3
- 1/cost^2-1 если t=1/3
- 1/(cos(t)^2)-1 при t=1/3
- 1 разделить на (cos(t)^2)-1 если t=1 разделить на 3
-
Похожие выражения
- 1/(cos(t)^2)+1 если t=1/3
1/(cos(t)^2)-1 если t=1/3
Решение
Вы ввели
[src]
1
1*------- - 1
2
cos (t)
$$\left(-1\right) 1 + 1 \cdot \frac{1}{\cos^{2}{\left(t \right)}}$$
1/cos(t)^2 - 1*1
Разложение дроби
[src]
-1 + cos(t)^(-2)
$$-1 + \frac{1}{\cos^{2}{\left(t \right)}}$$
1
-1 + -------
2
cos (t)
Подстановка условия
[src]
1/cos(t)^2 - 1*1 при t = 1/3
подставляем
1
1*------- - 1
2
cos (t)
$$\left(-1\right) 1 + 1 \cdot \frac{1}{\cos^{2}{\left(t \right)}}$$
2 tan (t)
$$\tan^{2}{\left(t \right)}$$
переменные
t = 1/3
$$t = \frac{1}{3}$$
2 tan ((1/3))
$$\tan^{2}{\left((1/3) \right)}$$
2 tan (1/3)
$$\tan^{2}{\left(\frac{1}{3} \right)}$$
tan(1/3)^2
Собрать выражение
[src]
2 -1 + sec (t)
$$\sec^{2}{\left(t \right)} - 1$$
1
-1 + -------
2
cos (t)
$$-1 + \frac{1}{\cos^{2}{\left(t \right)}}$$
-1 + cos(t)^(-2)
Комбинаторика
[src]
-(1 + cos(t))*(-1 + cos(t))
----------------------------
2
cos (t)
$$- \frac{\left(\cos{\left(t \right)} - 1\right) \left(\cos{\left(t \right)} + 1\right)}{\cos^{2}{\left(t \right)}}$$
-(1 + cos(t))*(-1 + cos(t))/cos(t)^2
Общий знаменатель
[src]
1
-1 + -------
2
cos (t)
$$-1 + \frac{1}{\cos^{2}{\left(t \right)}}$$
-1 + cos(t)^(-2)
Объединение рациональных выражений
[src]
2
1 - cos (t)
-----------
2
cos (t)
$$\frac{- \cos^{2}{\left(t \right)} + 1}{\cos^{2}{\left(t \right)}}$$
(1 - cos(t)^2)/cos(t)^2
Тригонометрическая часть
[src]
2 tan (t)
$$\tan^{2}{\left(t \right)}$$
2 -1 + sec (t)
$$\sec^{2}{\left(t \right)} - 1$$
1 ------- 2 cot (t)
$$\frac{1}{\cot^{2}{\left(t \right)}}$$
1
-1 + -------
2
cos (t)
$$-1 + \frac{1}{\cos^{2}{\left(t \right)}}$$
2/pi \
-1 + csc |-- - t|
\2 /
$$\csc^{2}{\left(- t + \frac{\pi}{2} \right)} - 1$$
1
-1 + ------------
2/ pi\
sin |t + --|
\ 2 /
$$-1 + \frac{1}{\sin^{2}{\left(t + \frac{\pi}{2} \right)}}$$
4 4*sin (t) --------- 2 sin (2*t)
$$\frac{4 \sin^{4}{\left(t \right)}}{\sin^{2}{\left(2 t \right)}}$$
1 - cos(2*t) ------------ 1 + cos(2*t)
$$\frac{- \cos{\left(2 t \right)} + 1}{\cos{\left(2 t \right)} + 1}$$
2
sec (t)
------------
2/ pi\
sec |t - --|
\ 2 /
$$\frac{\sec^{2}{\left(t \right)}}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}}$$
2/ pi\
cos |t - --|
\ 2 /
------------
2
cos (t)
$$\frac{\cos^{2}{\left(t - \frac{\pi}{2} \right)}}{\cos^{2}{\left(t \right)}}$$
2/pi \
csc |-- - t|
\2 /
------------
2
csc (t)
$$\frac{\csc^{2}{\left(- t + \frac{\pi}{2} \right)}}{\csc^{2}{\left(t \right)}}$$
2
/ 2/t\\
|1 + cot |-||
\ \2//
-1 + ---------------
2
/ 2/t\\
|-1 + cot |-||
\ \2//
$$-1 + \frac{\left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{t}{2} \right)} - 1\right)^{2}}$$
2
/ 2/t\\
|1 + tan |-||
\ \2//
-1 + --------------
2
/ 2/t\\
|1 - tan |-||
\ \2//
$$-1 + \frac{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}}{\left(- \tan^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}}$$
// 1 for t mod 2*pi = 0\
|| |
|| 1 |
-1 + |<------- otherwise |
|| 2 |
||cos (t) |
\\ /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{1}{\cos^{2}{\left(t \right)}} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
-1 + |< 2 |
||------------ otherwise |
\\1 + cos(2*t) /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{2}{\cos{\left(2 t \right)} + 1} & \text{otherwise} \end{cases}\right) - 1$$
2
/ 2/t pi\\
|1 + tan |- + --||
\ \2 4 //
-1 + -------------------
2/t pi\
4*tan |- + --|
\2 4 /
$$\frac{\left(\tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{4 \tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}} - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
-1 + |<------------ otherwise |
|| 1 |
||1 + -------- |
\\ sec(2*t) /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{2}{1 + \frac{1}{\sec{\left(2 t \right)}}} & \text{otherwise} \end{cases}\right) - 1$$
2
/ 1 \
|1 + -------|
| 2/t\|
| cot |-||
\ \2//
-1 + --------------
2
/ 1 \
|1 - -------|
| 2/t\|
| cot |-||
\ \2//
$$-1 + \frac{\left(1 + \frac{1}{\cot^{2}{\left(\frac{t}{2} \right)}}\right)^{2}}{\left(1 - \frac{1}{\cot^{2}{\left(\frac{t}{2} \right)}}\right)^{2}}$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
-1 + |<----------------- otherwise |
|| /pi \ |
||1 + sin|-- + 2*t| |
\\ \2 / /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{2}{\sin{\left(2 t + \frac{\pi}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
||----------------- otherwise |
-1 + |< 1 |
||1 + ------------- |
|| /pi \ |
|| csc|-- - 2*t| |
\\ \2 / /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{2}{1 + \frac{1}{\csc{\left(- 2 t + \frac{\pi}{2} \right)}}} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
||--------------- otherwise |
-1 + |< 2 |
|| 1 - tan (t) |
||1 + ----------- |
|| 2 |
\\ 1 + tan (t) /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{2}{\frac{- \tan^{2}{\left(t \right)} + 1}{\tan^{2}{\left(t \right)} + 1} + 1} & \text{otherwise} \end{cases}\right) - 1$$
2
/ 4/t\\
| 4*sin |-||
| \2/|
|1 + ---------|
| 2 |
\ sin (t) /
-1 + ----------------
2
/ 4/t\\
| 4*sin |-||
| \2/|
|1 - ---------|
| 2 |
\ sin (t) /
$$-1 + \frac{\left(\frac{4 \sin^{4}{\left(\frac{t}{2} \right)}}{\sin^{2}{\left(t \right)}} + 1\right)^{2}}{\left(- \frac{4 \sin^{4}{\left(\frac{t}{2} \right)}}{\sin^{2}{\left(t \right)}} + 1\right)^{2}}$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
|| / 2/t\\ |
|| |1 + cot |-|| |
-1 + |< \ \2// |
||--------------- otherwise |
|| 2 |
||/ 2/t\\ |
|||-1 + cot |-|| |
\\\ \2// /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{t}{2} \right)} - 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
-1 + |<--------------------------------- otherwise |
|| // 1 for t mod pi = 0\ |
||1 + |< | |
\\ \\cos(2*t) otherwise / /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{2}{\left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\cos{\left(2 t \right)} & \text{otherwise} \end{cases}\right) + 1} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
|| / 1 \ |
|| |1 + -------| |
|| | 2/t\| |
|| | tan |-|| |
-1 + |< \ \2// |
||--------------- otherwise |
|| 2 |
||/ 1 \ |
|||-1 + -------| |
||| 2/t\| |
||| tan |-|| |
\\\ \2// /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\left(1 + \frac{1}{\tan^{2}{\left(\frac{t}{2} \right)}}\right)^{2}}{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{t}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// / pi\ \
|| zoo for |t + --| mod pi = 0|
|| \ 2 / |
|| |
|| 2/t pi\ |
-1 + |< tan |- + --| |
|| \2 4 / |
||------------- otherwise |
|| 2 |
||(1 + sin(t)) |
\\ /
$$\left(\begin{cases} \tilde{\infty} & \text{for}\: \left(t + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{\tan^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}}{\left(\sin{\left(t \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
2
/ 2/t pi\\
| cos |- - --||
| \2 2 /|
|1 + ------------|
| 2/t\ |
| cos |-| |
\ \2/ /
-1 + -------------------
2
/ 2/t pi\\
| cos |- - --||
| \2 2 /|
|1 - ------------|
| 2/t\ |
| cos |-| |
\ \2/ /
$$-1 + \frac{\left(1 + \frac{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} \right)}}\right)^{2}}{\left(1 - \frac{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} \right)}}\right)^{2}}$$
2
/ 2/t\ \
| sec |-| |
| \2/ |
|1 + ------------|
| 2/t pi\|
| sec |- - --||
\ \2 2 //
-1 + -------------------
2
/ 2/t\ \
| sec |-| |
| \2/ |
|1 - ------------|
| 2/t pi\|
| sec |- - --||
\ \2 2 //
$$-1 + \frac{\left(\frac{\sec^{2}{\left(\frac{t}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\left(- \frac{\sec^{2}{\left(\frac{t}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}$$
2
/ 2/pi t\\
| csc |-- - -||
| \2 2/|
|1 + ------------|
| 2/t\ |
| csc |-| |
\ \2/ /
-1 + -------------------
2
/ 2/pi t\\
| csc |-- - -||
| \2 2/|
|1 - ------------|
| 2/t\ |
| csc |-| |
\ \2/ /
$$-1 + \frac{\left(1 + \frac{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{t}{2} \right)}}\right)^{2}}{\left(1 - \frac{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{t}{2} \right)}}\right)^{2}}$$
// / pi\ \
|| zoo for |t + --| mod pi = 0|
|| \ 2 / |
|| |
|| 2 |
||/ 2/t pi\\ |
-1 + |<|1 + cot |- + --|| |
||\ \2 4 // |
||------------------- otherwise |
|| 2/t pi\ |
|| 4*cot |- + --| |
|| \2 4 / |
\\ /
$$\left(\begin{cases} \tilde{\infty} & \text{for}\: \left(t + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{4 \cot^{2}{\left(\frac{t}{2} + \frac{\pi}{4} \right)}} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
||------------------------------------- otherwise |
|| // 1 for t mod pi = 0\ |
-1 + |< || | |
|| || 2 | |
||1 + |<-1 + cot (t) | |
|| ||------------ otherwise | |
|| || 2 | |
\\ \\1 + cot (t) / /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{2}{\left(\begin{cases} 1 & \text{for}\: t \bmod \pi = 0 \\\frac{\cot^{2}{\left(t \right)} - 1}{\cot^{2}{\left(t \right)} + 1} & \text{otherwise} \end{cases}\right) + 1} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
||/ 2 4/t\\ |
|||sin (t) + 4*sin |-|| |
-1 + |<\ \2// |
||---------------------- otherwise |
|| 2 |
||/ 2 4/t\\ |
|||sin (t) - 4*sin |-|| |
\\\ \2// /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\left(4 \sin^{4}{\left(\frac{t}{2} \right)} + \sin^{2}{\left(t \right)}\right)^{2}}{\left(- 4 \sin^{4}{\left(\frac{t}{2} \right)} + \sin^{2}{\left(t \right)}\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
|| / 2 \ |
|| | sin (t) | |
|| |1 + ---------| |
|| | 4/t\| |
|| | 4*sin |-|| |
-1 + |< \ \2// |
||----------------- otherwise |
|| 2 |
||/ 2 \ |
||| sin (t) | |
|||-1 + ---------| |
||| 4/t\| |
||| 4*sin |-|| |
\\\ \2// /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\left(1 + \frac{\sin^{2}{\left(t \right)}}{4 \sin^{4}{\left(\frac{t}{2} \right)}}\right)^{2}}{\left(-1 + \frac{\sin^{2}{\left(t \right)}}{4 \sin^{4}{\left(\frac{t}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
||/ 2/t\ \ |
||| cos |-| | |
||| \2/ | |
|||1 + ------------| |
||| 2/t pi\| |
||| cos |- - --|| |
-1 + |<\ \2 2 // |
||-------------------- otherwise |
|| 2 |
||/ 2/t\ \ |
||| cos |-| | |
||| \2/ | |
|||-1 + ------------| |
||| 2/t pi\| |
||| cos |- - --|| |
\\\ \2 2 // /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\left(\frac{\cos^{2}{\left(\frac{t}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\left(\frac{\cos^{2}{\left(\frac{t}{2} \right)}}{\cos^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
||/ 2/t pi\\ |
||| sec |- - --|| |
||| \2 2 /| |
|||1 + ------------| |
||| 2/t\ | |
||| sec |-| | |
-1 + |<\ \2/ / |
||-------------------- otherwise |
|| 2 |
||/ 2/t pi\\ |
||| sec |- - --|| |
||| \2 2 /| |
|||-1 + ------------| |
||| 2/t\ | |
||| sec |-| | |
\\\ \2/ / /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\left(1 + \frac{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} \right)}}\right)^{2}}{\left(-1 + \frac{\sec^{2}{\left(\frac{t}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{t}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for t mod 2*pi = 0\
|| |
|| 2 |
||/ 2/t\ \ |
||| csc |-| | |
||| \2/ | |
|||1 + ------------| |
||| 2/pi t\| |
||| csc |-- - -|| |
-1 + |<\ \2 2// |
||-------------------- otherwise |
|| 2 |
||/ 2/t\ \ |
||| csc |-| | |
||| \2/ | |
|||-1 + ------------| |
||| 2/pi t\| |
||| csc |-- - -|| |
\\\ \2 2// /
$$\left(\begin{cases} 1 & \text{for}\: t \bmod 2 \pi = 0 \\\frac{\left(\frac{\csc^{2}{\left(\frac{t}{2} \right)}}{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2}}{\left(\frac{\csc^{2}{\left(\frac{t}{2} \right)}}{\csc^{2}{\left(- \frac{t}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
-1 + Piecewise((1, Mod(t = 2*pi, 0)), ((1 + csc(t/2)^2/csc(pi/2 - t/2)^2)^2/(-1 + csc(t/2)^2/csc(pi/2 - t/2)^2)^2, True))
Рациональный знаменатель
[src]
1
-1 + -------
2
cos (t)
$$-1 + \frac{1}{\cos^{2}{\left(t \right)}}$$
2
1 - cos (t)
-----------
2
cos (t)
$$\frac{- \cos^{2}{\left(t \right)} + 1}{\cos^{2}{\left(t \right)}}$$
(1 - cos(t)^2)/cos(t)^2
Степени
[src]
1
-1 + -------
2
cos (t)
$$-1 + \frac{1}{\cos^{2}{\left(t \right)}}$$
1
-1 + ---------------
2
/ I*t -I*t\
|e e |
|---- + -----|
\ 2 2 /
$$-1 + \frac{1}{\left(\frac{e^{i t}}{2} + \frac{e^{- i t}}{2}\right)^{2}}$$
-1 + (exp(i*t)/2 + exp(-i*t)/2)^(-2)