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sin(165)+cos(195*c)*tan(255) если c=-1/4
Решение
Вы ввели
[src]
sin(165) + cos(195*c)*tan(255)
$$\cos{\left(195 c \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$
sin(165) + cos(195*c)*tan(255)
Подстановка условия
[src]
sin(165) + cos(195*c)*tan(255) при c = -1/4
подставляем
sin(165) + cos(195*c)*tan(255)
$$\cos{\left(195 c \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$
cos(195*c)*tan(255) + sin(165)
$$\cos{\left(195 c \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$
переменные
c = -1/4
$$c = - \frac{1}{4}$$
cos(195*(-1/4))*tan(255) + sin(165)
$$\cos{\left(195 (-1/4) \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$
cos(195/4)*tan(255) + sin(165)
$$\cos{\left(\frac{195}{4} \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$
cos(195/4)*tan(255) + sin(165)
Тригонометрическая часть
[src]
2 2*sin (255)*cos(195*c)*csc(510) + sin(165)
$$2 \sin^{2}{\left(255 \right)} \cos{\left(195 c \right)} \csc{\left(510 \right)} + \sin{\left(165 \right)}$$
cos(195*c)*sin(255)
------------------- + sin(165)
cos(255)
$$\frac{\sin{\left(255 \right)} \cos{\left(195 c \right)}}{\cos{\left(255 \right)}} + \sin{\left(165 \right)}$$
/ 2/195*c\\ |1 - 2*sin |-----||*tan(255) + sin(165) \ \ 2 //
$$\left(- 2 \sin^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \tan{\left(255 \right)} + \sin{\left(165 \right)}$$
2
2*sin (255)*cos(195*c)
---------------------- + sin(165)
sin(510)
$$\frac{2 \sin^{2}{\left(255 \right)} \cos{\left(195 c \right)}}{\sin{\left(510 \right)}} + \sin{\left(165 \right)}$$
1 sec(255) -------- + ------------------- csc(165) csc(255)*sec(195*c)
$$\frac{1}{\csc{\left(165 \right)}} + \frac{\sec{\left(255 \right)}}{\csc{\left(255 \right)} \sec{\left(195 c \right)}}$$
1 2*csc(510)
-------- + --------------------
csc(165) 2
csc (255)*sec(195*c)
$$\frac{1}{\csc{\left(165 \right)}} + \frac{2 \csc{\left(510 \right)}}{\csc^{2}{\left(255 \right)} \sec{\left(195 c \right)}}$$
(1 + cos(165))*tan(165/2) + cos(195*c)*tan(255)
$$\cos{\left(195 c \right)} \tan{\left(255 \right)} + \left(\cos{\left(165 \right)} + 1\right) \tan{\left(\frac{165}{2} \right)}$$
2 /pi \
2*sin (255)*sin|-- + 195*c|
\2 /
--------------------------- + sin(165)
sin(510)
$$\frac{2 \sin^{2}{\left(255 \right)} \sin{\left(195 c + \frac{\pi}{2} \right)}}{\sin{\left(510 \right)}} + \sin{\left(165 \right)}$$
/pi \
sin(255)*sin|-- + 195*c|
\2 /
------------------------ + sin(165)
/ pi\
sin|255 + --|
\ 2 /
$$\frac{\sin{\left(255 \right)} \sin{\left(195 c + \frac{\pi}{2} \right)}}{\sin{\left(\frac{\pi}{2} + 255 \right)}} + \sin{\left(165 \right)}$$
1 2*csc(510)
-------- + -------------------------
csc(165) 2 /pi \
csc (255)*csc|-- - 195*c|
\2 /
$$\frac{1}{\csc{\left(165 \right)}} + \frac{2 \csc{\left(510 \right)}}{\csc^{2}{\left(255 \right)} \csc{\left(- 195 c + \frac{\pi}{2} \right)}}$$
/ pi\
cos(195*c)*cos|255 - --|
\ 2 / / pi\
------------------------ + cos|165 - --|
cos(255) \ 2 /
$$\frac{\cos{\left(195 c \right)} \cos{\left(- \frac{\pi}{2} + 255 \right)}}{\cos{\left(255 \right)}} + \cos{\left(- \frac{\pi}{2} + 165 \right)}$$
1 sec(255) -------------- + ------------------------- / pi\ / pi\ sec|-165 + --| sec(195*c)*sec|-255 + --| \ 2 / \ 2 /
$$\frac{1}{\sec{\left(-165 + \frac{\pi}{2} \right)}} + \frac{\sec{\left(255 \right)}}{\sec{\left(195 c \right)} \sec{\left(-255 + \frac{\pi}{2} \right)}}$$
/ pi\
csc|-255 + --|
1 \ 2 /
-------- + ------------------------
csc(165) /pi \
csc(255)*csc|-- - 195*c|
\2 /
$$\frac{1}{\csc{\left(165 \right)}} + \frac{\csc{\left(-255 + \frac{\pi}{2} \right)}}{\csc{\left(255 \right)} \csc{\left(- 195 c + \frac{\pi}{2} \right)}}$$
1 sec(255) ------------- + ------------------------ / pi\ / pi\ sec|165 - --| sec(195*c)*sec|255 - --| \ 2 / \ 2 /
$$\frac{1}{\sec{\left(- \frac{\pi}{2} + 165 \right)}} + \frac{\sec{\left(255 \right)}}{\sec{\left(195 c \right)} \sec{\left(- \frac{\pi}{2} + 255 \right)}}$$
2 / 2/195*c\\
2*sin (255)*|1 - 2*sin |-----||
\ \ 2 //
------------------------------- + sin(165)
sin(510)
$$\frac{2 \cdot \left(- 2 \sin^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \sin^{2}{\left(255 \right)}}{\sin{\left(510 \right)}} + \sin{\left(165 \right)}$$
/ pi\
csc|-255 + --|
1 \ 2 /
-------------- + ------------------------------
csc(-165 + pi) /pi \
csc(-255 + pi)*csc|-- - 195*c|
\2 /
$$\frac{1}{\csc{\left(-165 + \pi \right)}} + \frac{\csc{\left(-255 + \frac{\pi}{2} \right)}}{\csc{\left(-255 + \pi \right)} \csc{\left(- 195 c + \frac{\pi}{2} \right)}}$$
2/ pi\
2*cos |255 - --|*cos(195*c)
\ 2 / / pi\
--------------------------- + cos|165 - --|
/ pi\ \ 2 /
cos|510 - --|
\ 2 /
$$\frac{2 \cos{\left(195 c \right)} \cos^{2}{\left(- \frac{\pi}{2} + 255 \right)}}{\cos{\left(- \frac{\pi}{2} + 510 \right)}} + \cos{\left(- \frac{\pi}{2} + 165 \right)}$$
/ 2 \ / pi\
|1 - -----------|*csc|-255 + --|
| 2/195*c\| \ 2 /
| csc |-----||
1 \ \ 2 //
-------- + --------------------------------
csc(165) csc(255)
$$\frac{\left(1 - \frac{2}{\csc^{2}{\left(\frac{195 c}{2} \right)}}\right) \csc{\left(-255 + \frac{\pi}{2} \right)}}{\csc{\left(255 \right)}} + \frac{1}{\csc{\left(165 \right)}}$$
/ pi\
2*sec|510 - --|
1 \ 2 /
------------- + -------------------------
/ pi\ 2/ pi\
sec|165 - --| sec(195*c)*sec |255 - --|
\ 2 / \ 2 /
$$\frac{1}{\sec{\left(- \frac{\pi}{2} + 165 \right)}} + \frac{2 \sec{\left(- \frac{\pi}{2} + 510 \right)}}{\sec{\left(195 c \right)} \sec^{2}{\left(- \frac{\pi}{2} + 255 \right)}}$$
// 1 for 195*c mod 2*pi = 0\ |< |*tan(255) + sin(165) \\cos(195*c) otherwise /
$$\left(\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \sin{\left(165 \right)}$$
-sin(90) - sin(15*(-17 + 13*c)) + sin(420) + sin(15*(17 + 13*c))
----------------------------------------------------------------
2*cos(255)
$$\frac{- \sin{\left(15 \cdot \left(13 c - 17\right) \right)} + \sin{\left(15 \cdot \left(13 c + 17\right) \right)} - \sin{\left(90 \right)} + \sin{\left(420 \right)}}{2 \cos{\left(255 \right)}}$$
/ 2/ pi 195*c\\ / pi\
|1 - 2*cos |- -- + -----||*cos|255 - --|
\ \ 2 2 // \ 2 / / pi\
---------------------------------------- + cos|165 - --|
cos(255) \ 2 /
$$\frac{\left(- 2 \cos^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)} + 1\right) \cos{\left(- \frac{\pi}{2} + 255 \right)}}{\cos{\left(255 \right)}} + \cos{\left(- \frac{\pi}{2} + 165 \right)}$$
/ 2 \
|1 - ------------------|*sec(255)
| 2/ pi 195*c\|
| sec |- -- + -----||
1 \ \ 2 2 //
------------- + ---------------------------------
/ pi\ / pi\
sec|165 - --| sec|255 - --|
\ 2 / \ 2 /
$$\frac{\left(1 - \frac{2}{\sec^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}}\right) \sec{\left(255 \right)}}{\sec{\left(- \frac{\pi}{2} + 255 \right)}} + \frac{1}{\sec{\left(- \frac{\pi}{2} + 165 \right)}}$$
/ 2/195*c\\
|1 - tan |-----||*tan(255)
2*tan(165/2) \ \ 2 //
--------------- + --------------------------
2 2/195*c\
1 + tan (165/2) 1 + tan |-----|
\ 2 /
$$\frac{\left(- \tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \tan{\left(255 \right)}}{\tan^{2}{\left(\frac{195 c}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$
2 // 1 for 195*c mod 2*pi = 0\
2*sin (255)*|< |
\\cos(195*c) otherwise /
------------------------------------------------- + sin(165)
sin(510)
$$\left(\frac{2 \left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(255 \right)}}{\sin{\left(510 \right)}}\right) + \sin{\left(165 \right)}$$
1 - cos(165) // 1 for 195*c mod 2*pi = 0\ ------------ + |< |*tan(255) tan(165/2) \\cos(195*c) otherwise /
$$\left(\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \frac{- \cos{\left(165 \right)} + 1}{\tan{\left(\frac{165}{2} \right)}}$$
/ 2/195*c\ \ | 8*tan |-----| | | \ 4 / | 2*tan(165/2) |1 - ------------------|*tan(255) + --------------- | 2| 2 | / 2/195*c\\ | 1 + tan (165/2) | |1 + tan |-----|| | \ \ \ 4 // /
$$\left(1 - \frac{8 \tan^{2}{\left(\frac{195 c}{4} \right)}}{\left(\tan^{2}{\left(\frac{195 c}{4} \right)} + 1\right)^{2}}\right) \tan{\left(255 \right)} + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$
// 1 for 195*c mod 2*pi = 0\
2 || |
2*sin (255)*|< /pi \ |
||sin|-- + 195*c| otherwise |
\\ \2 / /
------------------------------------------------------ + sin(165)
sin(510)
$$\left(\frac{2 \left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\sin{\left(195 c + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(255 \right)}}{\sin{\left(510 \right)}}\right) + \sin{\left(165 \right)}$$
/ // 195*c \\ | || 0 for ----- mod pi = 0|| | || 2 || |1 - 2*|< ||*tan(255) + sin(165) | ||1 - cos(195*c) || | ||-------------- otherwise || \ \\ 2 //
$$\left(\left(\left(- 2 \left(\begin{cases} 0 & \text{for}\: \frac{195 c}{2} \bmod \pi = 0 \\\frac{- \cos{\left(195 c \right)} + 1}{2} & \text{otherwise} \end{cases}\right)\right) + 1\right) \tan{\left(255 \right)}\right) + \sin{\left(165 \right)}$$
// 1 for 195*c mod 2*pi = 0\ / pi\
|< |*cos|255 - --|
\\cos(195*c) otherwise / \ 2 / / pi\
--------------------------------------------------- + cos|165 - --|
cos(255) \ 2 /
$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases}\right) \cos{\left(- \frac{\pi}{2} + 255 \right)}}{\cos{\left(255 \right)}}\right) + \cos{\left(- \frac{\pi}{2} + 165 \right)}$$
1
1 - -----------
2/195*c\
cot |-----|
2 \ 2 /
---------------------------- + --------------------------
/ 1 \ / 1 \
|1 + -----------|*cot(165/2) |1 + -----------|*cot(255)
| 2 | | 2/195*c\|
\ cot (165/2)/ | cot |-----||
\ \ 2 //
$$\frac{1 - \frac{1}{\cot^{2}{\left(\frac{195 c}{2} \right)}}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{195 c}{2} \right)}}\right) \cot{\left(255 \right)}} + \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{165}{2} \right)}}\right) \cot{\left(\frac{165}{2} \right)}}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|
$$\left(\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \sin{\left(165 \right)}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|| 1 | / pi\
|<--------------- otherwise |*csc|-255 + --|
|| /pi \ | \ 2 /
||csc|-- - 195*c| |
1 \\ \2 / /
-------- + ---------------------------------------------------------
csc(165) csc(255)
$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- 195 c + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \csc{\left(-255 + \frac{\pi}{2} \right)}}{\csc{\left(255 \right)}}\right) + \frac{1}{\csc{\left(165 \right)}}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|< 1 |*sec(255)
||---------- otherwise |
1 \\sec(195*c) /
------------- + ----------------------------------------------
/ pi\ / pi\
sec|165 - --| sec|255 - --|
\ 2 / \ 2 /
$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(195 c \right)}} & \text{otherwise} \end{cases}\right) \sec{\left(255 \right)}}{\sec{\left(- \frac{\pi}{2} + 255 \right)}}\right) + \frac{1}{\sec{\left(- \frac{\pi}{2} + 165 \right)}}$$
// /pi \ \ || 0 for |-- + 195*c| mod pi = 0| || \2 / | || | |< 1 + sin(195*c) |*tan(255) + sin(165) ||--------------- otherwise | || /pi 195*c\ | ||tan|-- + -----| | \\ \4 2 / /
$$\left(\left(\begin{cases} 0 & \text{for}\: \left(195 c + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{\sin{\left(195 c \right)} + 1}{\tan{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)}} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \sin{\left(165 \right)}$$
4 2/195*c\ 2 / 2 \ / 2/195*c\\
4*cos (255/2)*cos |-----|*tan (255/2)*\1 + tan (255)/*|1 - tan |-----||
\ 2 / \ \ 2 //
----------------------------------------------------------------------- + sin(165)
tan(255)
$$\frac{4 \cdot \left(- \tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \left(\tan^{2}{\left(255 \right)} + 1\right) \cos^{4}{\left(\frac{255}{2} \right)} \cos^{2}{\left(\frac{195 c}{2} \right)} \tan^{2}{\left(\frac{255}{2} \right)}}{\tan{\left(255 \right)}} + \sin{\left(165 \right)}$$
2 // 1 for 195*c mod 2*pi = 0\
4*tan (255/2)*|< |
\\cos(195*c) otherwise /
- --------------------------------------------------- + sin(165)
/ 4 \
\-1 + tan (255/2)/*sin(255)
$$\left(- \frac{4 \left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases}\right) \tan^{2}{\left(\frac{255}{2} \right)}}{\left(-1 + \tan^{4}{\left(\frac{255}{2} \right)}\right) \sin{\left(255 \right)}}\right) + \sin{\left(165 \right)}$$
4 2 / 2 \ /pi 195*c\
8*cos (255/2)*tan (255/2)*\1 + tan (255)/*tan|-- + -----|
\4 2 /
--------------------------------------------------------- + sin(165)
/ 2/pi 195*c\\
|1 + tan |-- + -----||*tan(255)
\ \4 2 //
$$\sin{\left(165 \right)} + \frac{8 \left(\tan^{2}{\left(255 \right)} + 1\right) \cos^{4}{\left(\frac{255}{2} \right)} \tan^{2}{\left(\frac{255}{2} \right)} \tan{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(255 \right)}}$$
/ 2/195*c\\
2*|1 - tan |-----||*tan(255/2)
2*tan(165/2) \ \ 2 //
--------------- + -----------------------------------
2 / 2/195*c\\ / 2 \
1 + tan (165/2) |1 + tan |-----||*\1 - tan (255/2)/
\ \ 2 //
$$\frac{2 \cdot \left(- \tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \tan{\left(\frac{255}{2} \right)}}{\left(- \tan^{2}{\left(\frac{255}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right)} + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$
/ 1 for 195*c mod 2*pi = 0
|
| 2/195*c\
|-1 + cot |-----|
< \ 2 /
|---------------- otherwise
| 2/195*c\
|1 + cot |-----|
\ \ 2 / 2*cot(165/2)
----------------------------------------- + ---------------
cot(255) 2
1 + cot (165/2)
$$\left(\frac{\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{195 c}{2} \right)} - 1}{\cot^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases}}{\cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$
// 1 for 195*c mod 2*pi = 0\ || | || 2/195*c\ | ||1 - tan |-----| | 2*tan(165/2) |< \ 2 / |*tan(255) + --------------- ||--------------- otherwise | 2 || 2/195*c\ | 1 + tan (165/2) ||1 + tan |-----| | \\ \ 2 / /
$$\left(\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{195 c}{2} \right)} + 1}{\tan^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$
// 1 for 195*c mod 2*pi = 0\ || | || 1 | ||-1 + ----------- | || 2/195*c\ | || tan |-----| | 2 |< \ 2 / |*tan(255) + ---------------------------- ||---------------- otherwise | / 1 \ || 1 | |1 + -----------|*tan(165/2) ||1 + ----------- | | 2 | || 2/195*c\ | \ tan (165/2)/ || tan |-----| | \\ \ 2 / /
$$\left(\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{195 c}{2} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{195 c}{2} \right)}}} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \frac{2}{\left(\frac{1}{\tan^{2}{\left(\frac{165}{2} \right)}} + 1\right) \tan{\left(\frac{165}{2} \right)}}$$
// 195*c \
|| 0 for ----- mod pi = 0|
|| 2 |
|| |
|| 2/195*c\ |
|| 4*cot |-----| |
1 - 2*|< \ 4 / |
||------------------ otherwise |
|| 2 |
||/ 2/195*c\\ |
|||1 + cot |-----|| |
||\ \ 4 // |
\\ / 2*cot(165/2)
------------------------------------------------- + ---------------
cot(255) 2
1 + cot (165/2)
$$\left(\frac{\left(- 2 \left(\begin{cases} 0 & \text{for}\: \frac{195 c}{2} \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{195 c}{4} \right)}}{\left(\cot^{2}{\left(\frac{195 c}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1}{\cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$
2 / 2 \ / 2/195*c\\
4*tan (255/2)*\1 + tan (255)/*|1 - tan |-----||
2*tan(165/2) \ \ 2 //
--------------- + -----------------------------------------------
2 2
1 + tan (165/2) / 2 \ / 2/195*c\\
\1 + tan (255/2)/ *|1 + tan |-----||*tan(255)
\ \ 2 //
$$\frac{4 \cdot \left(- \tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \left(\tan^{2}{\left(255 \right)} + 1\right) \tan^{2}{\left(\frac{255}{2} \right)}}{\left(1 + \tan^{2}{\left(\frac{255}{2} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \tan{\left(255 \right)}} + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$
2 / 2 \ /pi 195*c\
8*tan (255/2)*\1 + tan (255)/*tan|-- + -----|
2*tan(165/2) \4 2 /
--------------- + --------------------------------------------------
2 2
1 + tan (165/2) / 2 \ / 2/pi 195*c\\
\1 + tan (255/2)/ *|1 + tan |-- + -----||*tan(255)
\ \4 2 //
$$\frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}} + \frac{8 \left(\tan^{2}{\left(255 \right)} + 1\right) \tan^{2}{\left(\frac{255}{2} \right)} \tan{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)}}{\left(1 + \tan^{2}{\left(\frac{255}{2} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(255 \right)}}$$
2 / 2 4/195*c\\
2*sin (255)*|sin (195*c) - 4*sin |-----||
4*sin(165) \ \ 2 //
--------------------------- + -----------------------------------------
2 / 2 4/195*c\\
2 sin (165) |sin (195*c) + 4*sin |-----||*sin(510)
4*sin (165/2) + ----------- \ \ 2 //
2
sin (165/2)
$$\frac{2 \left(- 4 \sin^{4}{\left(\frac{195 c}{2} \right)} + \sin^{2}{\left(195 c \right)}\right) \sin^{2}{\left(255 \right)}}{\left(4 \sin^{4}{\left(\frac{195 c}{2} \right)} + \sin^{2}{\left(195 c \right)}\right) \sin{\left(510 \right)}} + \frac{4 \sin{\left(165 \right)}}{\frac{\sin^{2}{\left(165 \right)}}{\sin^{2}{\left(\frac{165}{2} \right)}} + 4 \sin^{2}{\left(\frac{165}{2} \right)}}$$
/ 1 for 195*c mod 2*pi = 0
|
|/ 1 for 195*c mod 2*pi = 0
||
|| 2/195*c\
<|-1 + cot |-----|
|< \ 2 / otherwise
||---------------- otherwise
|| 2/195*c\
||1 + cot |-----|
\\ \ 2 / 2*cot(165/2)
------------------------------------------------------------------ + ---------------
cot(255) 2
1 + cot (165/2)
$$\left(\frac{\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{195 c}{2} \right)} - 1}{\cot^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}}{\cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$
/ 4/195*c\\
| 4*sin |-----||
2 | \ 2 /|
2*sin (255)*|1 - -------------|
2 | 2 |
4*sin (165/2) \ sin (195*c) /
---------------------------- + -------------------------------
/ 4 \ / 4/195*c\\
| 4*sin (165/2)| | 4*sin |-----||
|1 + -------------|*sin(165) | \ 2 /|
| 2 | |1 + -------------|*sin(510)
\ sin (165) / | 2 |
\ sin (195*c) /
$$\frac{2 \left(- \frac{4 \sin^{4}{\left(\frac{195 c}{2} \right)}}{\sin^{2}{\left(195 c \right)}} + 1\right) \sin^{2}{\left(255 \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{195 c}{2} \right)}}{\sin^{2}{\left(195 c \right)}} + 1\right) \sin{\left(510 \right)}} + \frac{4 \sin^{2}{\left(\frac{165}{2} \right)}}{\left(1 + \frac{4 \sin^{4}{\left(\frac{165}{2} \right)}}{\sin^{2}{\left(165 \right)}}\right) \sin{\left(165 \right)}}$$
/ 2/255 pi\\ /pi 195*c\
2*|1 + tan |--- + --||*cot(255/2)*tan|-- + -----|
2*cot(165/2) \ \ 2 4 // \4 2 /
--------------- + ------------------------------------------------------
2 / 2 \ / 2/pi 195*c\\ /255 pi\
1 + cot (165/2) \1 + cot (255/2)/*|1 + tan |-- + -----||*tan|--- + --|
\ \4 2 // \ 2 4 /
$$\frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1} + \frac{2 \left(\tan^{2}{\left(\frac{\pi}{4} + \frac{255}{2} \right)} + 1\right) \tan{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)} \cot{\left(\frac{255}{2} \right)}}{\left(\tan^{2}{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(\frac{255}{2} \right)} + 1\right) \tan{\left(\frac{\pi}{4} + \frac{255}{2} \right)}}$$
/ 2/165 pi\\ 2/195*c\ / 2/255 pi\\ / 2/195*c\\
|1 - cot |--- + --||*(1 + sin(165)) cos |-----|*|1 - cot |--- + --||*|1 - tan |-----||*(1 + sin(255))
\ \ 2 4 // \ 2 / \ \ 2 4 // \ \ 2 //
----------------------------------- + -----------------------------------------------------------------
2 / 2 \ 2
2*\1 - tan (255/2)/*cos (255/2)
$$\frac{\left(- \tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \left(- \cot^{2}{\left(\frac{\pi}{4} + \frac{255}{2} \right)} + 1\right) \left(\sin{\left(255 \right)} + 1\right) \cos^{2}{\left(\frac{195 c}{2} \right)}}{2 \cdot \left(- \tan^{2}{\left(\frac{255}{2} \right)} + 1\right) \cos^{2}{\left(\frac{255}{2} \right)}} + \frac{\left(- \cot^{2}{\left(\frac{\pi}{4} + \frac{165}{2} \right)} + 1\right) \left(\sin{\left(165 \right)} + 1\right)}{2}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|| 2/195*c\ |
2 / 2 \ ||-1 + cot |-----| |
4*cot (255/2)*\1 + cot (255)/*|< \ 2 / |
||---------------- otherwise |
|| 2/195*c\ |
||1 + cot |-----| |
2*cot(165/2) \\ \ 2 / /
--------------- + -------------------------------------------------------------------------
2 2
1 + cot (165/2) / 2 \
\1 + cot (255/2)/ *cot(255)
$$\left(\frac{4 \cdot \left(1 + \cot^{2}{\left(255 \right)}\right) \left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{195 c}{2} \right)} - 1}{\cot^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \cot^{2}{\left(\frac{255}{2} \right)}}{\left(\cot^{2}{\left(\frac{255}{2} \right)} + 1\right)^{2} \cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$
// 1 for 195*c mod 2*pi = 0\
|| |
2 || -2 - 2*cos(390*c) + 4*cos(195*c) |
2*sin (255)*|<------------------------------------ otherwise |
|| 2 |
||1 - cos(390*c) + 2*(1 - cos(195*c)) |
\\ / 8*sin(165)
--------------------------------------------------------------------------- + --------------------------------
sin(510) / 2 \
| sin (165) |
(1 - cos(165))*|4 + -----------|
| 4 |
\ sin (165/2)/
$$\left(\frac{2 \left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{4 \cos{\left(195 c \right)} - 2 \cos{\left(390 c \right)} - 2}{2 \left(- \cos{\left(195 c \right)} + 1\right)^{2} - \cos{\left(390 c \right)} + 1} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(255 \right)}}{\sin{\left(510 \right)}}\right) + \frac{8 \sin{\left(165 \right)}}{\left(- \cos{\left(165 \right)} + 1\right) \left(\frac{\sin^{2}{\left(165 \right)}}{\sin^{4}{\left(\frac{165}{2} \right)}} + 4\right)}$$
2/165 pi\ / 2 \ / 2/195*c\\ / 2/255 pi\\
-1 + tan |--- + --| \1 + cot (255/2)/*|-1 + cot |-----||*|-1 + tan |--- + --||
\ 2 4 / \ \ 2 // \ \ 2 4 //
------------------- + ----------------------------------------------------------
2/165 pi\ / 2/195*c\\ / 2/255 pi\\ / 2 \
1 + tan |--- + --| |1 + cot |-----||*|1 + tan |--- + --||*\-1 + cot (255/2)/
\ 2 4 / \ \ 2 // \ \ 2 4 //
$$\frac{\left(-1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{255}{2} \right)}\right) \left(\cot^{2}{\left(\frac{255}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{195 c}{2} \right)} - 1\right)}{\left(-1 + \cot^{2}{\left(\frac{255}{2} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{4} + \frac{255}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{195 c}{2} \right)} + 1\right)} + \frac{-1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{165}{2} \right)}}$$
2/165 pi\ / 2 \ / 2/255 pi\\ / 2/195*c\\
1 - cot |--- + --| \1 + tan (255/2)/*|1 - cot |--- + --||*|1 - tan |-----||
\ 2 4 / \ \ 2 4 // \ \ 2 //
------------------ + --------------------------------------------------------
2/165 pi\ / 2/255 pi\\ / 2/195*c\\ / 2 \
1 + cot |--- + --| |1 + cot |--- + --||*|1 + tan |-----||*\1 - tan (255/2)/
\ 2 4 / \ \ 2 4 // \ \ 2 //
$$\frac{\left(1 + \tan^{2}{\left(\frac{255}{2} \right)}\right) \left(- \tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \left(- \cot^{2}{\left(\frac{\pi}{4} + \frac{255}{2} \right)} + 1\right)}{\left(- \tan^{2}{\left(\frac{255}{2} \right)} + 1\right) \left(1 + \cot^{2}{\left(\frac{\pi}{4} + \frac{255}{2} \right)}\right) \left(\tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right)} + \frac{- \cot^{2}{\left(\frac{\pi}{4} + \frac{165}{2} \right)} + 1}{\cot^{2}{\left(\frac{\pi}{4} + \frac{165}{2} \right)} + 1}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|| 2 |
|| sin (195*c) |
||-1 + ------------- |
|| 4/195*c\ |
2 || 4*sin |-----| |
2*sin (255)*|< \ 2 / |
||------------------ otherwise |
|| 2 |
|| sin (195*c) |
||1 + ------------- |
|| 4/195*c\ |
|| 4*sin |-----| |
sin(165) \\ \ 2 / /
------------------------------- + ---------------------------------------------------------
/ 2 \ sin(510)
| sin (165) | 2
|1 + -------------|*sin (165/2)
| 4 |
\ 4*sin (165/2)/
$$\left(\frac{2 \left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(195 c \right)}}{4 \sin^{4}{\left(\frac{195 c}{2} \right)}}}{1 + \frac{\sin^{2}{\left(195 c \right)}}{4 \sin^{4}{\left(\frac{195 c}{2} \right)}}} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(255 \right)}}{\sin{\left(510 \right)}}\right) + \frac{\sin{\left(165 \right)}}{\left(\frac{\sin^{2}{\left(165 \right)}}{4 \sin^{4}{\left(\frac{165}{2} \right)}} + 1\right) \sin^{2}{\left(\frac{165}{2} \right)}}$$
// /pi \ \
|| 0 for |-- + 195*c| mod pi = 0|
|| \2 / |
|| |
2 / 2 \ || /pi 195*c\ |
4*cot (255/2)*\1 + cot (255)/*|< 2*cot|-- + -----| |
|| \4 2 / |
||-------------------- otherwise |
|| 2/pi 195*c\ |
||1 + cot |-- + -----| |
2*cot(165/2) \\ \4 2 / /
--------------- + ----------------------------------------------------------------------------------
2 2
1 + cot (165/2) / 2 \
\1 + cot (255/2)/ *cot(255)
$$\left(\frac{4 \cdot \left(1 + \cot^{2}{\left(255 \right)}\right) \left(\begin{cases} 0 & \text{for}\: \left(195 c + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{195 c}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) \cot^{2}{\left(\frac{255}{2} \right)}}{\left(\cot^{2}{\left(\frac{255}{2} \right)} + 1\right)^{2} \cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$
/ 2/ pi 195*c\\
| cos |- -- + -----||
| \ 2 2 /| / pi\
|1 - ------------------|*cos|255 - --|
/165 pi\ | 2/195*c\ | \ 2 /
2*cos|--- - --| | cos |-----| |
\ 2 2 / \ \ 2 / /
------------------------------- + --------------------------------------
/ 2/165 pi\\ / 2/ pi 195*c\\
| cos |--- - --|| | cos |- -- + -----||
| \ 2 2 /| | \ 2 2 /|
|1 + --------------|*cos(165/2) |1 + ------------------|*cos(255)
| 2 | | 2/195*c\ |
\ cos (165/2) / | cos |-----| |
\ \ 2 / /
$$\frac{\left(1 - \frac{\cos^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{195 c}{2} \right)}}\right) \cos{\left(- \frac{\pi}{2} + 255 \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{195 c}{2} \right)}}\right) \cos{\left(255 \right)}} + \frac{2 \cos{\left(- \frac{\pi}{2} + \frac{165}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(- \frac{\pi}{2} + \frac{165}{2} \right)}}{\cos^{2}{\left(\frac{165}{2} \right)}}\right) \cos{\left(\frac{165}{2} \right)}}$$
/ 2/195*c\ \
| sec |-----| |
| \ 2 / |
|1 - ------------------|*sec(255)
| 2/ pi 195*c\|
| sec |- -- + -----||
2*sec(165/2) \ \ 2 2 //
---------------------------------- + --------------------------------------
/ 2 \ / 2/195*c\ \
| sec (165/2) | /165 pi\ | sec |-----| |
|1 + --------------|*sec|--- - --| | \ 2 / | / pi\
| 2/165 pi\| \ 2 2 / |1 + ------------------|*sec|255 - --|
| sec |--- - --|| | 2/ pi 195*c\| \ 2 /
\ \ 2 2 // | sec |- -- + -----||
\ \ 2 2 //
$$\frac{\left(- \frac{\sec^{2}{\left(\frac{195 c}{2} \right)}}{\sec^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(255 \right)}}{\left(\frac{\sec^{2}{\left(\frac{195 c}{2} \right)}}{\sec^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(- \frac{\pi}{2} + 255 \right)}} + \frac{2 \sec{\left(\frac{165}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{165}{2} \right)}}{\sec^{2}{\left(- \frac{\pi}{2} + \frac{165}{2} \right)}}\right) \sec{\left(- \frac{\pi}{2} + \frac{165}{2} \right)}}$$
/ 2/pi 195*c\\
| csc |-- - -----||
| \2 2 /| / pi\
|1 - ----------------|*csc|-255 + --|
/ 165 pi\ | 2/195*c\ | \ 2 /
2*csc|- --- + --| | csc |-----| |
\ 2 2 / \ \ 2 / /
--------------------------------- + -------------------------------------
/ 2/ 165 pi\\ / 2/pi 195*c\\
| csc |- --- + --|| | csc |-- - -----||
| \ 2 2 /| | \2 2 /|
|1 + ----------------|*csc(165/2) |1 + ----------------|*csc(255)
| 2 | | 2/195*c\ |
\ csc (165/2) / | csc |-----| |
\ \ 2 / /
$$\frac{\left(1 - \frac{\csc^{2}{\left(- \frac{195 c}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{195 c}{2} \right)}}\right) \csc{\left(-255 + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{195 c}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{195 c}{2} \right)}}\right) \csc{\left(255 \right)}} + \frac{2 \csc{\left(- \frac{165}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{165}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{165}{2} \right)}}\right) \csc{\left(\frac{165}{2} \right)}}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|| 2/195*c\ |
/ 2 \ / 2/255 pi\\ ||-1 + cot |-----| |
\1 + cot (255/2)/*|-1 + tan |--- + --||*|< \ 2 / |
\ \ 2 4 // ||---------------- otherwise |
2/165 pi\ || 2/195*c\ |
-1 + tan |--- + --| ||1 + cot |-----| |
\ 2 4 / \\ \ 2 / /
------------------- + -----------------------------------------------------------------------------------
2/165 pi\ / 2/255 pi\\ / 2 \
1 + tan |--- + --| |1 + tan |--- + --||*\-1 + cot (255/2)/
\ 2 4 / \ \ 2 4 //
$$\left(\frac{\left(-1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{255}{2} \right)}\right) \left(\cot^{2}{\left(\frac{255}{2} \right)} + 1\right) \left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{195 c}{2} \right)} - 1}{\cot^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)}{\left(-1 + \cot^{2}{\left(\frac{255}{2} \right)}\right) \left(\tan^{2}{\left(\frac{\pi}{4} + \frac{255}{2} \right)} + 1\right)}\right) + \frac{-1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{\pi}{4} + \frac{165}{2} \right)}}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|| 2/195*c\ |
|| cos |-----| |
|| \ 2 / |
||-1 + ------------------ |
|| 2/ pi 195*c\ |
|| cos |- -- + -----| | / pi\
|< \ 2 2 / |*cos|255 - --|
||----------------------- otherwise | \ 2 /
|| 2/195*c\ |
|| cos |-----| |
|| \ 2 / |
|| 1 + ------------------ |
|| 2/ pi 195*c\ |
|| cos |- -- + -----| |
\\ \ 2 2 / / 2*cos(165/2)
---------------------------------------------------------------- + ----------------------------------
cos(255) / 2 \
| cos (165/2) | /165 pi\
|1 + --------------|*cos|--- - --|
| 2/165 pi\| \ 2 2 /
| cos |--- - --||
\ \ 2 2 //
$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{\frac{\cos^{2}{\left(\frac{195 c}{2} \right)}}{\cos^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}} - 1}{\frac{\cos^{2}{\left(\frac{195 c}{2} \right)}}{\cos^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) \cos{\left(- \frac{\pi}{2} + 255 \right)}}{\cos{\left(255 \right)}}\right) + \frac{2 \cos{\left(\frac{165}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{165}{2} \right)}}{\cos^{2}{\left(- \frac{\pi}{2} + \frac{165}{2} \right)}} + 1\right) \cos{\left(- \frac{\pi}{2} + \frac{165}{2} \right)}}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|| 2/ pi 195*c\ |
|| sec |- -- + -----| |
|| \ 2 2 / |
||-1 + ------------------ |
|| 2/195*c\ |
|| sec |-----| |
|< \ 2 / |*sec(255)
||----------------------- otherwise |
|| 2/ pi 195*c\ |
|| sec |- -- + -----| |
|| \ 2 2 / |
|| 1 + ------------------ |
|| 2/195*c\ | /165 pi\
|| sec |-----| | 2*sec|--- - --|
\\ \ 2 / / \ 2 2 /
----------------------------------------------------------- + -------------------------------
/ pi\ / 2/165 pi\\
sec|255 - --| | sec |--- - --||
\ 2 / | \ 2 2 /|
|1 + --------------|*sec(165/2)
| 2 |
\ sec (165/2) /
$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{195 c}{2} \right)}}}{1 + \frac{\sec^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{195 c}{2} \right)}}} & \text{otherwise} \end{cases}\right) \sec{\left(255 \right)}}{\sec{\left(- \frac{\pi}{2} + 255 \right)}}\right) + \frac{2 \sec{\left(- \frac{\pi}{2} + \frac{165}{2} \right)}}{\left(\frac{\sec^{2}{\left(- \frac{\pi}{2} + \frac{165}{2} \right)}}{\sec^{2}{\left(\frac{165}{2} \right)}} + 1\right) \sec{\left(\frac{165}{2} \right)}}$$
// 1 for 195*c mod 2*pi = 0\
|| |
|| 2/195*c\ |
|| csc |-----| |
|| \ 2 / |
||-1 + ---------------- |
|| 2/pi 195*c\ |
|| csc |-- - -----| | / pi\
|< \2 2 / |*csc|-255 + --|
||--------------------- otherwise | \ 2 /
|| 2/195*c\ |
|| csc |-----| |
|| \ 2 / |
|| 1 + ---------------- |
|| 2/pi 195*c\ |
|| csc |-- - -----| |
\\ \2 2 / / 2*csc(165/2)
--------------------------------------------------------------- + --------------------------------------
csc(255) / 2 \
| csc (165/2) | / 165 pi\
|1 + ----------------|*csc|- --- + --|
| 2/ 165 pi\| \ 2 2 /
| csc |- --- + --||
\ \ 2 2 //
$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: 195 c \bmod 2 \pi = 0 \\\frac{\frac{\csc^{2}{\left(\frac{195 c}{2} \right)}}{\csc^{2}{\left(- \frac{195 c}{2} + \frac{\pi}{2} \right)}} - 1}{\frac{\csc^{2}{\left(\frac{195 c}{2} \right)}}{\csc^{2}{\left(- \frac{195 c}{2} + \frac{\pi}{2} \right)}} + 1} & \text{otherwise} \end{cases}\right) \csc{\left(-255 + \frac{\pi}{2} \right)}}{\csc{\left(255 \right)}}\right) + \frac{2 \csc{\left(\frac{165}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{165}{2} \right)}}{\csc^{2}{\left(- \frac{165}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{165}{2} + \frac{\pi}{2} \right)}}$$
Piecewise((1, Mod(195*c = 2*pi, 0)), ((-1 + csc(195*c/2)^2/csc(pi/2 - 195*c/2)^2)/(1 + csc(195*c/2)^2/csc(pi/2 - 195*c/2)^2), True))*csc(-255 + pi/2)/csc(255) + 2*csc(165/2)/((1 + csc(165/2)^2/csc(-165/2 + pi/2)^2)*csc(-165/2 + pi/2))
Численный ответ
[src]
0.997797279449891 + 0.58725445460932*cos(195*c)
0.997797279449891 + 0.58725445460932*cos(195*c)
Степени
[src]
/ -195*I*c 195*I*c\
|e e | / 255*I -255*I\
/ -165*I 165*I\ I*|--------- + --------|*\- e + e /
I*\- e + e / \ 2 2 /
- ---------------------- + ---------------------------------------------
2 -255*I 255*I
e + e
$$\frac{i \left(e^{- 255 i} - e^{255 i}\right) \left(\frac{e^{195 i c}}{2} + \frac{e^{- 195 i c}}{2}\right)}{e^{255 i} + e^{- 255 i}} - \frac{i \left(e^{165 i} - e^{- 165 i}\right)}{2}$$
-i*(-exp(-165*i) + exp(165*i))/2 + i*(exp(-195*i*c)/2 + exp(195*i*c)/2)*(-exp(255*i) + exp(-255*i))/(exp(-255*i) + exp(255*i))