Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- cos(b)^2-cos(b)^2*sin(b)^2 если b=1/3
- 5*sin(a)^2+5*cos(a)^2+3 если a=-1/2
- sin(2*pi+a)+cos(pi+a)-sin(-a)+cos(-a) если a=1/3
- b/(b-4*sqrt(b))-4*b^(3/2)/(b^2-16*b) если b=1
- Разложить многочлен на множители:
- z^d+3*d+15*z^n+45*n
- -16+49*y^2
- 22*x*y^2+33*x^2*y
- n^2-20*n-100
- Общий знаменатель:
- a-c/c-a-c/a+c
- ((sin(4*a)/(1+cos(4*a))))*((cos(2*a)/(1+cos(2*a))))
- t^2/4*a+t-16*a^2/4*a+t
- (sin((13*pi)/2-x)-cot(6*pi+x))/(1+sin(2*pi-x))
- Умножение столбиком:
- 16*35
- 76*53
- 98*49
- 36*45
- Деление столбиком:
- 52068/2
- 67800/5
- 2164/6
- 5256/7
- Раскрыть скобки в:
- (1-x)*(1-x)
- (-x-4)*(-x-4)
- a*(b-c)-b*(a-c)-c*(b-a)
- 5*b^2*c^3-2*b*c^2*k-5*c*k^2+2*k^2
- Разложение числа на простые множители:
- 4365
- 38250
- 22120
- 264
- График функции y =:
- -1/2
- Интеграл d{x}:
-
-1/2
- Производная:
- -1/2
-
Идентичные выражения
- пять *sin(a)^ два + пять *cos(a)^ два + три если a=- один / два
- 5 умножить на синус от (a) в квадрате плюс 5 умножить на косинус от (a) в квадрате плюс 3 если a равно минус 1 делить на 2
- пять умножить на синус от (a) в степени два плюс пять умножить на косинус от (a) в степени два плюс три если a равно минус один делить на два
- 5*sin(a)2+5*cos(a)2+3 если a=-1/2
- 5*sina2+5*cosa2+3 если a=-1/2
- 5*sin(a)²+5*cos(a)²+3 если a=-1/2
- 5*sin(a) в степени 2+5*cos(a) в степени 2+3 если a=-1/2
- 5sin(a)^2+5cos(a)^2+3 если a=-1/2
- 5sin(a)2+5cos(a)2+3 если a=-1/2
- 5sina2+5cosa2+3 если a=-1/2
- 5sina^2+5cosa^2+3 если a=-1/2
- 5*sin(a)^2+5*cos(a)^2+3 при a=-1/2
- 5*sin(a)^2+5*cos(a)^2+3 если a=-1 разделить на 2
-
Похожие выражения
- 5*sin(a)^2-5*cos(a)^2+3 если a=-1/2
- 5*sin(a)^2+5*cos(a)^2-3 если a=-1/2
- 5*sin(a)^2+5*cos(a)^2+3 если a=+1/2
5*sin(a)^2+5*cos(a)^2+3 если a=-1/2
Решение
Вы ввели
[src]
2 2 5*sin (a) + 5*cos (a) + 3
$$5 \sin^{2}{\left(a \right)} + 5 \cos^{2}{\left(a \right)} + 3$$
5*sin(a)^2 + 5*cos(a)^2 + 3
Тригонометрическая часть
[src]
8
$$8$$
5 5
3 + ------- + -------
2 2
csc (a) sec (a)
$$3 + \frac{5}{\sec^{2}{\left(a \right)}} + \frac{5}{\csc^{2}{\left(a \right)}}$$
2 2/ pi\
3 + 5*sin (a) + 5*sin |a + --|
\ 2 /
$$5 \sin^{2}{\left(a \right)} + 5 \sin^{2}{\left(a + \frac{\pi}{2} \right)} + 3$$
2 2/ pi\
3 + 5*cos (a) + 5*cos |a - --|
\ 2 /
$$5 \cos^{2}{\left(a \right)} + 5 \cos^{2}{\left(a - \frac{\pi}{2} \right)} + 3$$
5 5
3 + ------- + ------------
2 2/ pi\
sec (a) sec |a - --|
\ 2 /
$$3 + \frac{5}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + \frac{5}{\sec^{2}{\left(a \right)}}$$
5 5
3 + ------- + ------------
2 2/pi \
csc (a) csc |-- - a|
\2 /
$$3 + \frac{5}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{5}{\csc^{2}{\left(a \right)}}$$
5 5
3 + ------- + ------------
2 2/pi \
sec (a) sec |-- - a|
\2 /
$$3 + \frac{5}{\sec^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{5}{\sec^{2}{\left(a \right)}}$$
5 5
3 + ------------ + ------------
2 2/pi \
csc (pi - a) csc |-- - a|
\2 /
$$3 + \frac{5}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{5}{\csc^{2}{\left(- a + \pi \right)}}$$
31 2 5*cos(2*a) -- - 10*cos(a) - 5*(1 - cos(a)) + ---------- 2 2
$$- 5 \left(- \cos{\left(a \right)} + 1\right)^{2} - 10 \cos{\left(a \right)} + \frac{5 \cos{\left(2 a \right)}}{2} + \frac{31}{2}$$
2
/ 2/a pi\\ 2
5*|1 - cot |- + --|| *(1 + sin(a))
5*(1 + cos(2*a)) \ \2 4 //
3 + ---------------- + -----------------------------------
2 4
$$\frac{5 \left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\sin{\left(a \right)} + 1\right)^{2}}{4} + \frac{5 \left(\cos{\left(2 a \right)} + 1\right)}{2} + 3$$
2/a pi\
20*tan |- + --|
5*(1 - cos(2*a)) \2 4 /
3 + ---------------- + -------------------
2 2
/ 2/a pi\\
|1 + tan |- + --||
\ \2 4 //
$$\frac{5 \cdot \left(- \cos{\left(2 a \right)} + 1\right)}{2} + 3 + \frac{20 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$
2
/ 2/a\\ 2/a\
5*|1 - tan |-|| 20*tan |-|
\ \2// \2/
3 + ---------------- + --------------
2 2
/ 2/a\\ / 2/a\\
|1 + tan |-|| |1 + tan |-||
\ \2// \ \2//
$$\frac{5 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + 3 + \frac{20 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
2/a\ 2/a pi\
20*tan |-| 20*tan |- + --|
\2/ \2 4 /
3 + -------------- + -------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + tan |-|| |1 + tan |- + --||
\ \2// \ \2 4 //
$$3 + \frac{20 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{20 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
2/a\ 2/a pi\
20*cot |-| 20*tan |- + --|
\2/ \2 4 /
3 + -------------- + -------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + cot |-|| |1 + tan |- + --||
\ \2// \ \2 4 //
$$3 + \frac{20 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + \frac{20 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}$$
2
/ 1 \
5*|1 - -------|
| 2/a\|
| cot |-||
\ \2// 20
3 + ---------------- + ----------------------
2 2
/ 1 \ / 1 \ 2/a\
|1 + -------| |1 + -------| *cot |-|
| 2/a\| | 2/a\| \2/
| cot |-|| | cot |-||
\ \2// \ \2//
$$\frac{5 \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} + 3 + \frac{20}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cot^{2}{\left(\frac{a}{2} \right)}}$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
3 + 5*|< 2 | + 5*|< 2 |
||sin (a) otherwise | ||cos (a) otherwise |
\\ / \\ /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + 3$$
2 2
/ 2/a\\ / 2/a pi\\
5*|-1 + cot |-|| 5*|-1 + tan |- + --||
\ \2// \ \2 4 //
3 + ----------------- + ----------------------
2 2
/ 2/a\\ / 2/a pi\\
|1 + cot |-|| |1 + tan |- + --||
\ \2// \ \2 4 //
$$\frac{5 \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{5 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + 3$$
2 2
/ 2/a pi\\ / 2/a\\
5*|1 - cot |- + --|| 5*|1 - tan |-||
\ \2 4 // \ \2//
3 + --------------------- + ----------------
2 2
/ 2/a pi\\ / 2/a\\
|1 + cot |- + --|| |1 + tan |-||
\ \2 4 // \ \2//
$$\frac{5 \left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + \frac{5 \left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + 3$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
3 + 5*|< 2 | + 5*|< 2/ pi\ |
||sin (a) otherwise | ||sin |a + --| otherwise |
\\ / \\ \ 2 / /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\sin^{2}{\left(a + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
3 + 5*|< 2/ pi\ | + 5*|< 2 |
||cos |a - --| otherwise | ||cos (a) otherwise |
\\ \ 2 / / \\ /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\cos^{2}{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| 1 | || 1 |
3 + 5*|<------------ otherwise | + 5*|<------- otherwise |
|| 2/ pi\ | || 2 |
||sec |a - --| | ||sec (a) |
\\ \ 2 / / \\ /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\sec^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| 1 | || 1 |
3 + 5*|<------- otherwise | + 5*|<------------ otherwise |
|| 2 | || 2/pi \ |
||csc (a) | ||csc |-- - a| |
\\ / \\ \2 / /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\csc^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| | || \ 2 / |
3 + 5*|< 2 | + 5*|< |
||cos (a) otherwise | || 4/a\ 2/a\ |
\\ / ||- 4*cos |-| + 4*cos |-| otherwise |
\\ \2/ \2/ /
$$\left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + 3$$
2
/ 4/a\\
| 4*sin |-||
| \2/|
5*|1 - ---------| 4/a\
| 2 | 80*sin |-|
\ sin (a) / \2/
3 + ------------------ + ------------------------
2 2
/ 4/a\\ / 4/a\\
| 4*sin |-|| | 4*sin |-||
| \2/| | \2/| 2
|1 + ---------| |1 + ---------| *sin (a)
| 2 | | 2 |
\ sin (a) / \ sin (a) /
$$\frac{5 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2}} + 3 + \frac{80 \sin^{4}{\left(\frac{a}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right)^{2} \sin^{2}{\left(a \right)}}$$
// / pi\ \
// 0 for a mod pi = 0\ || 0 for |a + --| mod pi = 0|
|| | || \ 2 / |
3 + 5*|< 2 | + 5*|< |
||sin (a) otherwise | || 2 2/a pi\ |
\\ / ||(1 + sin(a)) *cot |- + --| otherwise |
\\ \2 4 / /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\left(\sin{\left(a \right)} + 1\right)^{2} \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
||/ 0 for a mod pi = 0 | ||/ 1 for a mod 2*pi = 0 |
3 + 5*|<| | + 5*|<| |
||< 2 otherwise | ||< 2 otherwise |
|||sin (a) otherwise | |||cos (a) otherwise |
\\\ / \\\ /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| 2/a\ | || 2 |
|| 4*cot |-| | ||/ 2/a\\ |
|| \2/ | |||-1 + cot |-|| |
3 + 5*|<-------------- otherwise | + 5*|<\ \2// |
|| 2 | ||--------------- otherwise |
||/ 2/a\\ | || 2 |
|||1 + cot |-|| | || / 2/a\\ |
||\ \2// | || |1 + cot |-|| |
\\ / \\ \ \2// /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
|| 2/a\ | || 2 |
|| 4*tan |-| | ||/ 2/a\\ |
|| \2/ | |||1 - tan |-|| |
3 + 5*|<-------------- otherwise | + 5*|<\ \2// |
|| 2 | ||-------------- otherwise |
||/ 2/a\\ | || 2 |
|||1 + tan |-|| | ||/ 2/a\\ |
||\ \2// | |||1 + tan |-|| |
\\ / \\\ \2// /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
2
/ 2/a pi\\
| cos |- - --||
| \2 2 /|
5*|1 - ------------|
| 2/a\ | 2/a pi\
| cos |-| | 20*cos |- - --|
\ \2/ / \2 2 /
3 + --------------------- + ---------------------------
2 2
/ 2/a pi\\ / 2/a pi\\
| cos |- - --|| | cos |- - --||
| \2 2 /| | \2 2 /| 2/a\
|1 + ------------| |1 + ------------| *cos |-|
| 2/a\ | | 2/a\ | \2/
| cos |-| | | cos |-| |
\ \2/ / \ \2/ /
$$\frac{5 \left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} + 3 + \frac{20 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \cos^{2}{\left(\frac{a}{2} \right)}}$$
2
/ 2/a\ \
| sec |-| |
| \2/ |
5*|1 - ------------|
| 2/a pi\| 2/a\
| sec |- - --|| 20*sec |-|
\ \2 2 // \2/
3 + --------------------- + --------------------------------
2 2
/ 2/a\ \ / 2/a\ \
| sec |-| | | sec |-| |
| \2/ | | \2/ | 2/a pi\
|1 + ------------| |1 + ------------| *sec |- - --|
| 2/a pi\| | 2/a pi\| \2 2 /
| sec |- - --|| | sec |- - --||
\ \2 2 // \ \2 2 //
$$\frac{5 \left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}} + 3 + \frac{20 \sec^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
2
/ 2/pi a\\
| csc |-- - -||
| \2 2/|
5*|1 - ------------|
| 2/a\ | 2/pi a\
| csc |-| | 20*csc |-- - -|
\ \2/ / \2 2/
3 + --------------------- + ---------------------------
2 2
/ 2/pi a\\ / 2/pi a\\
| csc |-- - -|| | csc |-- - -||
| \2 2/| | \2 2/| 2/a\
|1 + ------------| |1 + ------------| *csc |-|
| 2/a\ | | 2/a\ | \2/
| csc |-| | | csc |-| |
\ \2/ / \ \2/ /
$$\frac{5 \left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} + 3 + \frac{20 \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \csc^{2}{\left(\frac{a}{2} \right)}}$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 1 \ |
|| 4 | |||-1 + -------| |
||---------------------- otherwise | ||| 2/a\| |
|| 2 | ||| tan |-|| |
3 + 5*|
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \tan^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// / pi\ \
// 0 for a mod pi = 0\ || 0 for |a + --| mod pi = 0|
|| | || \ 2 / |
|| 2/a\ | || |
|| 4*cot |-| | || 2/a pi\ |
|| \2/ | || 4*cot |- + --| |
3 + 5*|<-------------- otherwise | + 5*|< \2 4 / |
|| 2 | ||------------------- otherwise |
||/ 2/a\\ | || 2 |
|||1 + cot |-|| | ||/ 2/a pi\\ |
||\ \2// | |||1 + cot |- + --|| |
\\ / ||\ \2 4 // |
\\ /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| | || \ 2 / |
|| 2 | || |
||/ 2/a\\ | || 2 |
|||-1 + cot |-|| | ||/ 2/a pi\\ |
3 + 5*|<\ \2// | + 5*|<|-1 + tan |- + --|| |
||--------------- otherwise | ||\ \2 4 // |
|| 2 | ||-------------------- otherwise |
|| / 2/a\\ | || 2 |
|| |1 + cot |-|| | ||/ 2/a pi\\ |
\\ \ \2// / |||1 + tan |- + --|| |
\\\ \2 4 // /
$$\left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 0 for a mod pi = 0\
|| | // 1 for a mod 2*pi = 0\
|| 2 | || |
|| sin (a) | || 2 |
||------------------------ otherwise | ||/ 2 4/a\\ |
|| 2 | |||sin (a) - 4*sin |-|| |
3 + 5*|
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin^{2}{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(- 4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}}{\left(4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 2 \ |
|| 2 | ||| sin (a) | |
|| sin (a) | |||-1 + ---------| |
||------------------------ otherwise | ||| 4/a\| |
|| 2 | ||| 4*sin |-|| |
3 + 5*|
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin^{2}{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 0 for a mod pi = 0\ // 1 for a mod 2*pi = 0\
|| | || |
||/ 0 for a mod pi = 0 | ||/ 1 for a mod 2*pi = 0 |
||| | ||| |
||| 2/a\ | ||| 2 |
||| 4*cot |-| | |||/ 2/a\\ |
3 + 5*|<| \2/ | + 5*|<||-1 + cot |-|| |
||<-------------- otherwise otherwise | ||<\ \2// otherwise |
||| 2 | |||--------------- otherwise |
|||/ 2/a\\ | ||| 2 |
||||1 + cot |-|| | ||| / 2/a\\ |
|||\ \2// | ||| |1 + cot |-|| |
\\\ / \\\ \ \2// /
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 2/a\ \ |
|| 2/a\ | ||| cos |-| | |
|| 4*cos |-| | ||| \2/ | |
|| \2/ | |||-1 + ------------| |
||-------------------------------- otherwise | ||| 2/a pi\| |
|| 2 | ||| cos |- - --|| |
3 + 5*|
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \cos^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 2/a pi\\ |
|| 2/a pi\ | ||| sec |- - --|| |
|| 4*sec |- - --| | ||| \2 2 /| |
|| \2 2 / | |||-1 + ------------| |
||--------------------------- otherwise | ||| 2/a\ | |
|| 2 | ||| sec |-| | |
3 + 5*|
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2} \sec^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
// 1 for a mod 2*pi = 0\
|| |
// 0 for a mod pi = 0\ || 2 |
|| | ||/ 2/a\ \ |
|| 2/a\ | ||| csc |-| | |
|| 4*csc |-| | ||| \2/ | |
|| \2/ | |||-1 + ------------| |
||-------------------------------- otherwise | ||| 2/pi a\| |
|| 2 | ||| csc |-- - -|| |
3 + 5*|
$$\left(5 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{4 \csc^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2} \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(5 \left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1\right)^{2}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 3$$
3 + 5*Piecewise((0, Mod(a = pi, 0)), (4*csc(a/2)^2/((1 + csc(a/2)^2/csc(pi/2 - a/2)^2)^2*csc(pi/2 - a/2)^2), True)) + 5*Piecewise((1, Mod(a = 2*pi, 0)), ((-1 + csc(a/2)^2/csc(pi/2 - a/2)^2)^2/(1 + csc(a/2)^2/csc(pi/2 - a/2)^2)^2, True))
Степени
[src]
2 2
/ I*a -I*a\ / -I*a I*a\
|e e | 5*\- e + e /
3 + 5*|---- + -----| - -------------------
\ 2 2 / 4
$$5 \left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{2} - \frac{5 \left(e^{i a} - e^{- i a}\right)^{2}}{4} + 3$$
3 + 5*(exp(i*a)/2 + exp(-i*a)/2)^2 - 5*(-exp(-i*a) + exp(i*a))^2/4