Господин Экзамен
cos(p2)-a если p2=3
Решение
Подстановка условия
[src]
cos(p2) - a при p2 = 3
подставляем
cos(p2) - a
$$- a + \cos{\left(p_{2} \right)}$$
-a + cos(p2)
$$- a + \cos{\left(p_{2} \right)}$$
переменные
p2 = 3
$$p_{2} = 3$$
-a + cos((3))
$$- a + \cos{\left((3) \right)}$$
-a + cos(3)
$$- a + \cos{\left(3 \right)}$$
-a + cos(3)
Степени
[src]
I*p2 -I*p2 e e ----- + ------ - a 2 2
$$- a + \frac{e^{i p_{2}}}{2} + \frac{e^{- i p_{2}}}{2}$$
exp(i*p2)/2 + exp(-i*p2)/2 - a
Тригонометрическая часть
[src]
1 ------- - a sec(p2)
$$- a + \frac{1}{\sec{\left(p_{2} \right)}}$$
/ pi\
-a + sin|p2 + --|
\ 2 /
$$- a + \sin{\left(p_{2} + \frac{\pi}{2} \right)}$$
2/p2\
-1 - a + 2*cos |--|
\2 /
$$2 \cos^{2}{\left(\frac{p_{2}}{2} \right)} - a - 1$$
1 ------------ - a /pi \ csc|-- - p2| \2 /
$$- a + \frac{1}{\csc{\left(- p_{2} + \frac{\pi}{2} \right)}}$$
2/p2\
-1 + cot |--|
\2 /
-a + -------------
2/p2\
1 + cot |--|
\2 /
$$- a + \frac{\cot^{2}{\left(\frac{p_{2}}{2} \right)} - 1}{\cot^{2}{\left(\frac{p_{2}}{2} \right)} + 1}$$
2/p2\
1 - tan |--|
\2 /
-a + ------------
2/p2\
1 + tan |--|
\2 /
$$- a + \frac{- \tan^{2}{\left(\frac{p_{2}}{2} \right)} + 1}{\tan^{2}{\left(\frac{p_{2}}{2} \right)} + 1}$$
1
1 - --------
2/p2\
cot |--|
\2 /
-a + ------------
1
1 + --------
2/p2\
cot |--|
\2 /
$$- a + \frac{1 - \frac{1}{\cot^{2}{\left(\frac{p_{2}}{2} \right)}}}{1 + \frac{1}{\cot^{2}{\left(\frac{p_{2}}{2} \right)}}}$$
/p2 pi\
2*tan|-- + --|
\2 4 /
-a + -----------------
2/p2 pi\
1 + tan |-- + --|
\2 4 /
$$- a + \frac{2 \tan{\left(\frac{p_{2}}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{p_{2}}{2} + \frac{\pi}{4} \right)} + 1}$$
// 1 for p2 mod 2*pi = 0\
-a + |< |
\\cos(p2) otherwise /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\cos{\left(p_{2} \right)} & \text{otherwise} \end{cases}\right)$$
2
a + cos (p2) - cos(p2) - a*cos(p2)
----------------------------------
-1 + cos(p2)
$$\frac{- a \cos{\left(p_{2} \right)} + \cos^{2}{\left(p_{2} \right)} + a - \cos{\left(p_{2} \right)}}{\cos{\left(p_{2} \right)} - 1}$$
// 1 for p2 mod 2*pi = 0\
|| |
-a + |< 1 |
||------- otherwise |
\\sec(p2) /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(p_{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
-a + |< / pi\ |
||sin|p2 + --| otherwise |
\\ \ 2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\sin{\left(p_{2} + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 1 |
-a + |<------------ otherwise |
|| /pi \ |
||csc|-- - p2| |
\\ \2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- p_{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
4/p2\
4*sin |--|
\2 /
1 - ----------
2
sin (p2)
-a + --------------
4/p2\
4*sin |--|
\2 /
1 + ----------
2
sin (p2)
$$- a + \frac{- \frac{4 \sin^{4}{\left(\frac{p_{2}}{2} \right)}}{\sin^{2}{\left(p_{2} \right)}} + 1}{\frac{4 \sin^{4}{\left(\frac{p_{2}}{2} \right)}}{\sin^{2}{\left(p_{2} \right)}} + 1}$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 2/p2\ |
||-1 + cot |--| |
-a + |< \2 / |
||------------- otherwise |
|| 2/p2\ |
|| 1 + cot |--| |
\\ \2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{p_{2}}{2} \right)} - 1}{\cot^{2}{\left(\frac{p_{2}}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 2/p2\ |
||1 - tan |--| |
-a + |< \2 / |
||------------ otherwise |
|| 2/p2\ |
||1 + tan |--| |
\\ \2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{p_{2}}{2} \right)} + 1}{\tan^{2}{\left(\frac{p_{2}}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
-a + |
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\cos{\left(p_{2} \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 1 |
||-1 + -------- |
|| 2/p2\ |
|| tan |--| |
-a + |< \2 / |
||------------- otherwise |
|| 1 |
|| 1 + -------- |
|| 2/p2\ |
|| tan |--| |
\\ \2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{p_{2}}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{p_{2}}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 0 for |p2 + --| mod pi = 0|
|| \ 2 / |
-a + |< |
|| /p2 pi\ |
||(1 + sin(p2))*cot|-- + --| otherwise |
\\ \2 4 / /
$$- a + \left(\begin{cases} 0 & \text{for}\: \left(p_{2} + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(p_{2} \right)} + 1\right) \cot{\left(\frac{p_{2}}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right)$$
2/p2 pi\
cos |-- - --|
\2 2 /
1 - -------------
2/p2\
cos |--|
\2 /
-a + -----------------
2/p2 pi\
cos |-- - --|
\2 2 /
1 + -------------
2/p2\
cos |--|
\2 /
$$- a + \frac{1 - \frac{\cos^{2}{\left(\frac{p_{2}}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{p_{2}}{2} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{p_{2}}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{p_{2}}{2} \right)}}}$$
2/p2\
sec |--|
\2 /
1 - -------------
2/p2 pi\
sec |-- - --|
\2 2 /
-a + -----------------
2/p2\
sec |--|
\2 /
1 + -------------
2/p2 pi\
sec |-- - --|
\2 2 /
$$- a + \frac{- \frac{\sec^{2}{\left(\frac{p_{2}}{2} \right)}}{\sec^{2}{\left(\frac{p_{2}}{2} - \frac{\pi}{2} \right)}} + 1}{\frac{\sec^{2}{\left(\frac{p_{2}}{2} \right)}}{\sec^{2}{\left(\frac{p_{2}}{2} - \frac{\pi}{2} \right)}} + 1}$$
2/pi p2\
csc |-- - --|
\2 2 /
1 - -------------
2/p2\
csc |--|
\2 /
-a + -----------------
2/pi p2\
csc |-- - --|
\2 2 /
1 + -------------
2/p2\
csc |--|
\2 /
$$- a + \frac{1 - \frac{\csc^{2}{\left(- \frac{p_{2}}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{p_{2}}{2} \right)}}}{1 + \frac{\csc^{2}{\left(- \frac{p_{2}}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{p_{2}}{2} \right)}}}$$
// / pi\ \
|| 0 for |p2 + --| mod pi = 0|
|| \ 2 / |
|| |
|| /p2 pi\ |
-a + |< 2*cot|-- + --| |
|| \2 4 / |
||----------------- otherwise |
|| 2/p2 pi\ |
||1 + cot |-- + --| |
\\ \2 4 / /
$$- a + \left(\begin{cases} 0 & \text{for}\: \left(p_{2} + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{p_{2}}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{p_{2}}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 2 |
-a + |< -4 + 4*sin (p2) + 4*cos(p2) |
||----------------------------- otherwise |
|| 2 2 |
\\2*(1 - cos(p2)) + 2*sin (p2) /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{4 \sin^{2}{\left(p_{2} \right)} + 4 \cos{\left(p_{2} \right)} - 4}{2 \left(- \cos{\left(p_{2} \right)} + 1\right)^{2} + 2 \sin^{2}{\left(p_{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 2 |
|| sin (p2) |
||-1 + ---------- |
|| 4/p2\ |
|| 4*sin |--| |
-a + |< \2 / |
||--------------- otherwise |
|| 2 |
|| sin (p2) |
|| 1 + ---------- |
|| 4/p2\ |
|| 4*sin |--| |
\\ \2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(p_{2} \right)}}{4 \sin^{4}{\left(\frac{p_{2}}{2} \right)}}}{1 + \frac{\sin^{2}{\left(p_{2} \right)}}{4 \sin^{4}{\left(\frac{p_{2}}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
||/ 1 for p2 mod 2*pi = 0 |
||| |
||| 2/p2\ |
-a + |<|-1 + cot |--| |
||< \2 / otherwise |
|||------------- otherwise |
||| 2/p2\ |
||| 1 + cot |--| |
\\\ \2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{p_{2}}{2} \right)} - 1}{\cot^{2}{\left(\frac{p_{2}}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 2/p2\ |
|| cos |--| |
|| \2 / |
||-1 + ------------- |
|| 2/p2 pi\ |
|| cos |-- - --| |
-a + |< \2 2 / |
||------------------ otherwise |
|| 2/p2\ |
|| cos |--| |
|| \2 / |
||1 + ------------- |
|| 2/p2 pi\ |
|| cos |-- - --| |
\\ \2 2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{p_{2}}{2} \right)}}{\cos^{2}{\left(\frac{p_{2}}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{p_{2}}{2} \right)}}{\cos^{2}{\left(\frac{p_{2}}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 2/p2 pi\ |
|| sec |-- - --| |
|| \2 2 / |
||-1 + ------------- |
|| 2/p2\ |
|| sec |--| |
-a + |< \2 / |
||------------------ otherwise |
|| 2/p2 pi\ |
|| sec |-- - --| |
|| \2 2 / |
||1 + ------------- |
|| 2/p2\ |
|| sec |--| |
\\ \2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{p_{2}}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{p_{2}}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{p_{2}}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{p_{2}}{2} \right)}}} & \text{otherwise} \end{cases}\right)$$
// 1 for p2 mod 2*pi = 0\
|| |
|| 2/p2\ |
|| csc |--| |
|| \2 / |
||-1 + ------------- |
|| 2/pi p2\ |
|| csc |-- - --| |
-a + |< \2 2 / |
||------------------ otherwise |
|| 2/p2\ |
|| csc |--| |
|| \2 / |
||1 + ------------- |
|| 2/pi p2\ |
|| csc |-- - --| |
\\ \2 2 / /
$$- a + \left(\begin{cases} 1 & \text{for}\: p_{2} \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{p_{2}}{2} \right)}}{\csc^{2}{\left(- \frac{p_{2}}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{p_{2}}{2} \right)}}{\csc^{2}{\left(- \frac{p_{2}}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
-a + Piecewise((1, Mod(p2 = 2*pi, 0)), ((-1 + csc(p2/2)^2/csc(pi/2 - p2/2)^2)/(1 + csc(p2/2)^2/csc(pi/2 - p2/2)^2), True))