Господин Экзамен
sin(7*a)+sin(a) если a=3
Решение
Вы ввели
[src]
sin(7*a) + sin(a)
$$\sin{\left(a \right)} + \sin{\left(7 a \right)}$$
sin(7*a) + sin(a)
Подстановка условия
[src]
sin(7*a) + sin(a) при a = 3
подставляем
sin(7*a) + sin(a)
$$\sin{\left(a \right)} + \sin{\left(7 a \right)}$$
sin(a) + sin(7*a)
$$\sin{\left(a \right)} + \sin{\left(7 a \right)}$$
переменные
a = 3
$$a = 3$$
sin((3)) + sin(7*(3))
$$\sin{\left((3) \right)} + \sin{\left(7 (3) \right)}$$
sin(3) + sin(7*3)
$$\sin{\left(3 \right)} + \sin{\left(7 \cdot 3 \right)}$$
sin(3) + sin(21)
$$\sin{\left(3 \right)} + \sin{\left(21 \right)}$$
sin(3) + sin(21)
Степени
[src]
/ -I*a I*a\ / -7*I*a 7*I*a\
I*\- e + e / I*\- e + e /
- ------------------ - ----------------------
2 2
$$- \frac{i \left(e^{i a} - e^{- i a}\right)}{2} - \frac{i \left(e^{7 i a} - e^{- 7 i a}\right)}{2}$$
-i*(-exp(-i*a) + exp(i*a))/2 - i*(-exp(-7*i*a) + exp(7*i*a))/2
Тригонометрическая часть
[src]
2*cos(3*a)*sin(4*a)
$$2 \sin{\left(4 a \right)} \cos{\left(3 a \right)}$$
1 1 ------ + -------- csc(a) csc(7*a)
$$\frac{1}{\csc{\left(7 a \right)}} + \frac{1}{\csc{\left(a \right)}}$$
/ pi\ / pi\ cos|a - --| + cos|7*a - --| \ 2 / \ 2 /
$$\cos{\left(a - \frac{\pi}{2} \right)} + \cos{\left(7 a - \frac{\pi}{2} \right)}$$
1 1 ----------- + ------------- csc(pi - a) csc(pi - 7*a)
$$\frac{1}{\csc{\left(- a + \pi \right)}} + \frac{1}{\csc{\left(- 7 a + \pi \right)}}$$
1 1 ----------- + ------------- / pi\ / pi\ sec|a - --| sec|7*a - --| \ 2 / \ 2 /
$$\frac{1}{\sec{\left(7 a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}$$
1 1 ----------- + ------------- /pi \ /pi \ sec|-- - a| sec|-- - 7*a| \2 / \2 /
$$\frac{1}{\sec{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(- 7 a + \frac{\pi}{2} \right)}}$$
/a\ /7*a\
(1 + cos(a))*tan|-| + (1 + cos(7*a))*tan|---|
\2/ \ 2 /
$$\left(\cos{\left(a \right)} + 1\right) \tan{\left(\frac{a}{2} \right)} + \left(\cos{\left(7 a \right)} + 1\right) \tan{\left(\frac{7 a}{2} \right)}$$
/a\ /7*a\
2*cot|-| 2*cot|---|
\2/ \ 2 /
----------- + -------------
2/a\ 2/7*a\
1 + cot |-| 1 + cot |---|
\2/ \ 2 /
$$\frac{2 \cot{\left(\frac{7 a}{2} \right)}}{\cot^{2}{\left(\frac{7 a}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}$$
/a\ /7*a\
2*tan|-| 2*tan|---|
\2/ \ 2 /
----------- + -------------
2/a\ 2/7*a\
1 + tan |-| 1 + tan |---|
\2/ \ 2 /
$$\frac{2 \tan{\left(\frac{7 a}{2} \right)}}{\tan^{2}{\left(\frac{7 a}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}$$
2 2 -------------------- + ------------------------ / 1 \ /a\ / 1 \ /7*a\ |1 + -------|*cot|-| |1 + ---------|*cot|---| | 2/a\| \2/ | 2/7*a\| \ 2 / | cot |-|| | cot |---|| \ \2// \ \ 2 //
$$\frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{7 a}{2} \right)}}\right) \cot{\left(\frac{7 a}{2} \right)}} + \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(\frac{a}{2} \right)}}$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ |< | + |< | \\sin(a) otherwise / \\sin(7*a) otherwise /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\sin{\left(7 a \right)} & \text{otherwise} \end{cases}\right)$$
2/a pi\ 2/pi 7*a\
-1 + tan |- + --| -1 + tan |-- + ---|
\2 4 / \4 2 /
----------------- + -------------------
2/a pi\ 2/pi 7*a\
1 + tan |- + --| 1 + tan |-- + ---|
\2 4 / \4 2 /
$$\frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} + \frac{\tan^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1}$$
/ 2/a pi\\ / 2/pi 7*a\\
|1 - cot |- + --||*(1 + sin(a)) |1 - cot |-- + ---||*(1 + sin(7*a))
\ \2 4 // \ \4 2 //
------------------------------- + -----------------------------------
2 2
$$\frac{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(a \right)} + 1\right)}{2} + \frac{\left(- \cot^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(7 a \right)} + 1\right)}{2}$$
2/a pi\ 2/pi 7*a\
1 - cot |- + --| 1 - cot |-- + ---|
\2 4 / \4 2 /
---------------- + ------------------
2/a pi\ 2/pi 7*a\
1 + cot |- + --| 1 + cot |-- + ---|
\2 4 / \4 2 /
$$\frac{- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} + \frac{- \cot^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1}$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | |< 1 | + |< 1 | ||------ otherwise | ||-------- otherwise | \\csc(a) / \\csc(7*a) /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\csc{\left(a \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{1}{\csc{\left(7 a \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | |< / pi\ | + |< / pi\ | ||cos|a - --| otherwise | ||cos|7*a - --| otherwise | \\ \ 2 / / \\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\cos{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\cos{\left(7 a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)$$
2/a\ 2/7*a\
4*sin |-|*sin(a) 4*sin |---|*sin(7*a)
\2/ \ 2 /
------------------- + -----------------------
2 4/a\ 2 4/7*a\
sin (a) + 4*sin |-| sin (7*a) + 4*sin |---|
\2/ \ 2 /
$$\frac{4 \sin^{2}{\left(\frac{7 a}{2} \right)} \sin{\left(7 a \right)}}{4 \sin^{4}{\left(\frac{7 a}{2} \right)} + \sin^{2}{\left(7 a \right)}} + \frac{4 \sin^{2}{\left(\frac{a}{2} \right)} \sin{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}}$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | || 1 | || 1 | |<----------- otherwise | + |<------------- otherwise | || / pi\ | || / pi\ | ||sec|a - --| | ||sec|7*a - --| | \\ \ 2 / / \\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{1}{\sec{\left(7 a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// / 3*pi\ \ // / 3*pi\ \ || 1 for |a + ----| mod 2*pi = 0| || 1 for |7*a + ----| mod 2*pi = 0| |< \ 2 / | + |< \ 2 / | || | || | \\sin(a) otherwise / \\sin(7*a) otherwise /
$$\left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: \left(7 a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(7 a \right)} & \text{otherwise} \end{cases}\right)$$
2/a\ 2/7*a\
4*sin |-| 4*sin |---|
\2/ \ 2 /
---------------------- + --------------------------
/ 4/a\\ / 4/7*a\\
| 4*sin |-|| | 4*sin |---||
| \2/| | \ 2 /|
|1 + ---------|*sin(a) |1 + -----------|*sin(7*a)
| 2 | | 2 |
\ sin (a) / \ sin (7*a) /
$$\frac{4 \sin^{2}{\left(\frac{7 a}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{7 a}{2} \right)}}{\sin^{2}{\left(7 a \right)}} + 1\right) \sin{\left(7 a \right)}} + \frac{4 \sin^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \sin{\left(a \right)}}$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | ||1 - cos(a) | ||1 - cos(7*a) | |<---------- otherwise | + |<------------ otherwise | || /a\ | || /7*a\ | || tan|-| | || tan|---| | \\ \2/ / \\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{- \cos{\left(a \right)} + 1}{\tan{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{- \cos{\left(7 a \right)} + 1}{\tan{\left(\frac{7 a}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | || /a\ | || /7*a\ | || 2*tan|-| | || 2*tan|---| | |< \2/ | + |< \ 2 / | ||----------- otherwise | ||------------- otherwise | || 2/a\ | || 2/7*a\ | ||1 + tan |-| | ||1 + tan |---| | \\ \2/ / \\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{7 a}{2} \right)}}{\tan^{2}{\left(\frac{7 a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | || /a\ | || /7*a\ | || 2*cot|-| | || 2*cot|---| | |< \2/ | + |< \ 2 / | ||----------- otherwise | ||------------- otherwise | || 2/a\ | || 2/7*a\ | ||1 + cot |-| | ||1 + cot |---| | \\ \2/ / \\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{7 a}{2} \right)}}{\cot^{2}{\left(\frac{7 a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\sin{\left(7 a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|| 2 | || 2 |
||-------------------- otherwise | ||------------------------ otherwise |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{7 a}{2} \right)}}\right) \tan{\left(\frac{7 a}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
/a\ /7*a\
2*sec|-| 2*sec|---|
\2/ \ 2 /
------------------------------ + --------------------------------------
/ 2/a\ \ / 2/7*a\ \
| sec |-| | | sec |---| |
| \2/ | /a pi\ | \ 2 / | / pi 7*a\
|1 + ------------|*sec|- - --| |1 + ----------------|*sec|- -- + ---|
| 2/a pi\| \2 2 / | 2/ pi 7*a\| \ 2 2 /
| sec |- - --|| | sec |- -- + ---||
\ \2 2 // \ \ 2 2 //
$$\frac{2 \sec{\left(\frac{7 a}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{7 a}{2} \right)}}{\sec^{2}{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}} + \frac{2 \sec{\left(\frac{a}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
/a pi\ / pi 7*a\
2*cos|- - --| 2*cos|- -- + ---|
\2 2 / \ 2 2 /
------------------------- + -------------------------------
/ 2/a pi\\ / 2/ pi 7*a\\
| cos |- - --|| | cos |- -- + ---||
| \2 2 /| /a\ | \ 2 2 /| /7*a\
|1 + ------------|*cos|-| |1 + ----------------|*cos|---|
| 2/a\ | \2/ | 2/7*a\ | \ 2 /
| cos |-| | | cos |---| |
\ \2/ / \ \ 2 / /
$$\frac{2 \cos{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{7 a}{2} \right)}}\right) \cos{\left(\frac{7 a}{2} \right)}} + \frac{2 \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos{\left(\frac{a}{2} \right)}}$$
/pi a\ /pi 7*a\
2*csc|-- - -| 2*csc|-- - ---|
\2 2/ \2 2 /
------------------------- + -----------------------------
/ 2/pi a\\ / 2/pi 7*a\\
| csc |-- - -|| | csc |-- - ---||
| \2 2/| /a\ | \2 2 /| /7*a\
|1 + ------------|*csc|-| |1 + --------------|*csc|---|
| 2/a\ | \2/ | 2/7*a\ | \ 2 /
| csc |-| | | csc |---| |
\ \2/ / \ \ 2 / /
$$\frac{2 \csc{\left(- \frac{7 a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{7 a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{7 a}{2} \right)}}\right) \csc{\left(\frac{7 a}{2} \right)}} + \frac{2 \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(\frac{a}{2} \right)}}$$
// 0 for a mod pi = 0\ || | || 2*sin(a) | // 0 for 7*a mod pi = 0\ ||---------------------------- otherwise | || | || / 2 \ | || -2*sin(14*a) + 4*sin(7*a) | |< | sin (a) | | + |<--------------------------------- otherwise | ||(1 - cos(a))*|1 + ---------| | || 2 | || | 4/a\| | ||1 - cos(14*a) + 2*(1 - cos(7*a)) | || | 4*sin |-|| | \\ / || \ \2// | \\ /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \sin{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(- \cos{\left(a \right)} + 1\right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{4 \sin{\left(7 a \right)} - 2 \sin{\left(14 a \right)}}{2 \left(- \cos{\left(7 a \right)} + 1\right)^{2} - \cos{\left(14 a \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// / 3*pi\ \ // / 3*pi\ \ || 1 for |a + ----| mod 2*pi = 0| || 1 for |7*a + ----| mod 2*pi = 0| || \ 2 / | || \ 2 / | || | || | || 2/a pi\ | || 2/pi 7*a\ | |<-1 + tan |- + --| | + |<-1 + tan |-- + ---| | || \2 4 / | || \4 2 / | ||----------------- otherwise | ||------------------- otherwise | || 2/a pi\ | || 2/pi 7*a\ | || 1 + tan |- + --| | || 1 + tan |-- + ---| | \\ \2 4 / / \\ \4 2 / /
$$\left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: \left(7 a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | || sin(a) | || sin(7*a) | ||----------------------- otherwise | ||--------------------------- otherwise | ||/ 2 \ | ||/ 2 \ | |<| sin (a) | 2/a\ | + |<| sin (7*a) | 2/7*a\ | |||1 + ---------|*sin |-| | |||1 + -----------|*sin |---| | ||| 4/a\| \2/ | ||| 4/7*a\| \ 2 / | ||| 4*sin |-|| | ||| 4*sin |---|| | ||\ \2// | ||\ \ 2 // | \\ / \\ /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{\sin{\left(7 a \right)}}{\left(1 + \frac{\sin^{2}{\left(7 a \right)}}{4 \sin^{4}{\left(\frac{7 a}{2} \right)}}\right) \sin^{2}{\left(\frac{7 a}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | ||/ 0 for a mod pi = 0 | ||/ 0 for 7*a mod pi = 0 | ||| | ||| | ||| /a\ | ||| /7*a\ | |<| 2*cot|-| | + |<| 2*cot|---| | ||< \2/ otherwise | ||< \ 2 / otherwise | |||----------- otherwise | |||------------- otherwise | ||| 2/a\ | ||| 2/7*a\ | |||1 + cot |-| | |||1 + cot |---| | \\\ \2/ / \\\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{7 a}{2} \right)}}{\cot^{2}{\left(\frac{7 a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|| /a\ | || /7*a\ |
|| 2*cos|-| | || 2*cos|---| |
|| \2/ | || \ 2 / |
||------------------------------ otherwise | ||-------------------------------------- otherwise |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{7 a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{7 a}{2} \right)}}{\cos^{2}{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|| /a pi\ | || / pi 7*a\ |
|| 2*sec|- - --| | || 2*sec|- -- + ---| |
|| \2 2 / | || \ 2 2 / |
||------------------------- otherwise | ||------------------------------- otherwise |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \sec{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{7 a}{2} \right)}}\right) \sec{\left(\frac{7 a}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|| /a\ | || /7*a\ |
|| 2*csc|-| | || 2*csc|---| |
|| \2/ | || \ 2 / |
||------------------------------ otherwise | ||---------------------------------- otherwise |
|
$$\left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{7 a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{7 a}{2} \right)}}{\csc^{2}{\left(- \frac{7 a}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{7 a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
Piecewise((0, Mod(a = pi, 0)), (2*csc(a/2)/((1 + csc(a/2)^2/csc(pi/2 - a/2)^2)*csc(pi/2 - a/2)), True)) + Piecewise((0, Mod(7*a = pi, 0)), (2*csc(7*a/2)/((1 + csc(7*a/2)^2/csc(pi/2 - 7*a/2)^2)*csc(pi/2 - 7*a/2)), True))