Господин Экзамен
cos(6*a)+1 если a=1
Решение
Подстановка условия
[src]
cos(6*a) + 1 при a = 1
подставляем
cos(6*a) + 1
$$\cos{\left(6 a \right)} + 1$$
1 + cos(6*a)
$$\cos{\left(6 a \right)} + 1$$
переменные
a = 1
$$a = 1$$
1 + cos(6*(1))
$$\cos{\left(6 (1) \right)} + 1$$
1 + cos(6*1)
$$\cos{\left(6 \cdot 1 \right)} + 1$$
1 + cos(6)
$$\cos{\left(6 \right)} + 1$$
1 + cos(6)
Степени
[src]
-6*I*a 6*I*a
e e
1 + ------- + ------
2 2
$$\frac{e^{6 i a}}{2} + 1 + \frac{e^{- 6 i a}}{2}$$
1 + exp(-6*i*a)/2 + exp(6*i*a)/2
Тригонометрическая часть
[src]
2 2*cos (3*a)
$$2 \cos^{2}{\left(3 a \right)}$$
1
1 + --------
sec(6*a)
$$1 + \frac{1}{\sec{\left(6 a \right)}}$$
/pi \
1 + sin|-- + 6*a|
\2 /
$$\sin{\left(6 a + \frac{\pi}{2} \right)} + 1$$
1
1 + -------------
/pi \
csc|-- - 6*a|
\2 /
$$1 + \frac{1}{\csc{\left(- 6 a + \frac{\pi}{2} \right)}}$$
2 2 1 + cos (3*a) - sin (3*a)
$$- \sin^{2}{\left(3 a \right)} + \cos^{2}{\left(3 a \right)} + 1$$
2
-1 + cot (3*a)
1 + --------------
2
1 + cot (3*a)
$$\frac{\cot^{2}{\left(3 a \right)} - 1}{\cot^{2}{\left(3 a \right)} + 1} + 1$$
2
1 - tan (3*a)
1 + -------------
2
1 + tan (3*a)
$$\frac{- \tan^{2}{\left(3 a \right)} + 1}{\tan^{2}{\left(3 a \right)} + 1} + 1$$
1
1 - ---------
2
cot (3*a)
1 + -------------
1
1 + ---------
2
cot (3*a)
$$\frac{1 - \frac{1}{\cot^{2}{\left(3 a \right)}}}{1 + \frac{1}{\cot^{2}{\left(3 a \right)}}} + 1$$
/ pi\
2*tan|3*a + --|
\ 4 /
1 + ------------------
2/ pi\
1 + tan |3*a + --|
\ 4 /
$$1 + \frac{2 \tan{\left(3 a + \frac{\pi}{4} \right)}}{\tan^{2}{\left(3 a + \frac{\pi}{4} \right)} + 1}$$
// 1 for 3*a mod pi = 0\
1 + |< |
\\cos(6*a) otherwise /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
1 + |< 1 |
||-------- otherwise |
\\sec(6*a) /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{1}{\sec{\left(6 a \right)}} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
1 + |< /pi \ |
||sin|-- + 6*a| otherwise |
\\ \2 / /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\sin{\left(6 a + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
|| 1 |
1 + |<------------- otherwise |
|| /pi \ |
||csc|-- - 6*a| |
\\ \2 / /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{1}{\csc{\left(- 6 a + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + 1$$
4
4*sin (3*a)
1 - -----------
2
sin (6*a)
1 + ---------------
4
4*sin (3*a)
1 + -----------
2
sin (6*a)
$$\frac{- \frac{4 \sin^{4}{\left(3 a \right)}}{\sin^{2}{\left(6 a \right)}} + 1}{\frac{4 \sin^{4}{\left(3 a \right)}}{\sin^{2}{\left(6 a \right)}} + 1} + 1$$
// 1 for 3*a mod pi = 0\
|| |
|| 2 |
1 + |<-1 + cot (3*a) |
||-------------- otherwise |
|| 2 |
\\1 + cot (3*a) /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(3 a \right)} - 1}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
|| 2 |
1 + |<1 - tan (3*a) |
||------------- otherwise |
|| 2 |
\\1 + tan (3*a) /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{- \tan^{2}{\left(3 a \right)} + 1}{\tan^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right) + 1$$
2/ pi\
cos |3*a - --|
\ 2 /
1 - --------------
2
cos (3*a)
1 + ------------------
2/ pi\
cos |3*a - --|
\ 2 /
1 + --------------
2
cos (3*a)
$$\frac{1 - \frac{\cos^{2}{\left(3 a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(3 a \right)}}}{1 + \frac{\cos^{2}{\left(3 a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(3 a \right)}}} + 1$$
2
sec (3*a)
1 - --------------
2/ pi\
sec |3*a - --|
\ 2 /
1 + ------------------
2
sec (3*a)
1 + --------------
2/ pi\
sec |3*a - --|
\ 2 /
$$\frac{- \frac{\sec^{2}{\left(3 a \right)}}{\sec^{2}{\left(3 a - \frac{\pi}{2} \right)}} + 1}{\frac{\sec^{2}{\left(3 a \right)}}{\sec^{2}{\left(3 a - \frac{\pi}{2} \right)}} + 1} + 1$$
2/pi \
csc |-- - 3*a|
\2 /
1 - --------------
2
csc (3*a)
1 + ------------------
2/pi \
csc |-- - 3*a|
\2 /
1 + --------------
2
csc (3*a)
$$\frac{1 - \frac{\csc^{2}{\left(- 3 a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(3 a \right)}}}{1 + \frac{\csc^{2}{\left(- 3 a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(3 a \right)}}} + 1$$
// 1 for 3*a mod pi = 0\
|| |
|| 1 |
||-1 + --------- |
|| 2 |
1 + |< tan (3*a) |
||-------------- otherwise |
|| 1 |
||1 + --------- |
|| 2 |
\\ tan (3*a) /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(3 a \right)}}}{1 + \frac{1}{\tan^{2}{\left(3 a \right)}}} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
1 + |
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + 1$$
// /pi \ \
|| 0 for |-- + 6*a| mod pi = 0|
|| \2 / |
1 + |< |
|| / pi\ |
||(1 + sin(6*a))*cot|3*a + --| otherwise |
\\ \ 4 / /
$$\left(\begin{cases} 0 & \text{for}\: \left(6 a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(6 a \right)} + 1\right) \cot{\left(3 a + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right) + 1$$
// /pi \ \
|| 0 for |-- + 6*a| mod pi = 0|
|| \2 / |
|| |
|| / pi\ |
1 + |< 2*cot|3*a + --| |
|| \ 4 / |
||------------------ otherwise |
|| 2/ pi\ |
||1 + cot |3*a + --| |
\\ \ 4 / /
$$\left(\begin{cases} 0 & \text{for}\: \left(6 a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(3 a + \frac{\pi}{4} \right)}}{\cot^{2}{\left(3 a + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
|| 2 |
|| sin (6*a) |
||-1 + ----------- |
|| 4 |
1 + |< 4*sin (3*a) |
||---------------- otherwise |
|| 2 |
|| sin (6*a) |
||1 + ----------- |
|| 4 |
\\ 4*sin (3*a) /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(6 a \right)}}{4 \sin^{4}{\left(3 a \right)}}}{1 + \frac{\sin^{2}{\left(6 a \right)}}{4 \sin^{4}{\left(3 a \right)}}} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
||/ 1 for 3*a mod pi = 0 |
||| |
1 + |<| 2 |
||<-1 + cot (3*a) otherwise |
|||-------------- otherwise |
||| 2 |
\\\1 + cot (3*a) /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(3 a \right)} - 1}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
|| 2 |
|| cos (3*a) |
||-1 + -------------- |
|| 2/ pi\ |
|| cos |3*a - --| |
1 + |< \ 2 / |
||------------------- otherwise |
|| 2 |
|| cos (3*a) |
|| 1 + -------------- |
|| 2/ pi\ |
|| cos |3*a - --| |
\\ \ 2 / /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{\frac{\cos^{2}{\left(3 a \right)}}{\cos^{2}{\left(3 a - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(3 a \right)}}{\cos^{2}{\left(3 a - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
|| 2/ pi\ |
|| sec |3*a - --| |
|| \ 2 / |
||-1 + -------------- |
|| 2 |
1 + |< sec (3*a) |
||------------------- otherwise |
|| 2/ pi\ |
|| sec |3*a - --| |
|| \ 2 / |
|| 1 + -------------- |
|| 2 |
\\ sec (3*a) /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(3 a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(3 a \right)}}}{1 + \frac{\sec^{2}{\left(3 a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(3 a \right)}}} & \text{otherwise} \end{cases}\right) + 1$$
// 1 for 3*a mod pi = 0\
|| |
|| 2 |
|| csc (3*a) |
||-1 + -------------- |
|| 2/pi \ |
|| csc |-- - 3*a| |
1 + |< \2 / |
||------------------- otherwise |
|| 2 |
|| csc (3*a) |
|| 1 + -------------- |
|| 2/pi \ |
|| csc |-- - 3*a| |
\\ \2 / /
$$\left(\begin{cases} 1 & \text{for}\: 3 a \bmod \pi = 0 \\\frac{\frac{\csc^{2}{\left(3 a \right)}}{\csc^{2}{\left(- 3 a + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(3 a \right)}}{\csc^{2}{\left(- 3 a + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) + 1$$
1 + Piecewise((1, Mod(3*a = pi, 0)), ((-1 + csc(3*a)^2/csc(pi/2 - 3*a)^2)/(1 + csc(3*a)^2/csc(pi/2 - 3*a)^2), True))