Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- g^3-p^2*g-p*g^2+p^3 если p=1/3
- 1/(1+tan(a)^2)+1/(1+cot(a)^2) если a=1/3
- 24*x^6-44*x^4*y-18*x^2*y^3+33*y^4 если y=1
- c^7-c^5 если c=-1/3
- Разложить многочлен на множители:
- 35*a^m+20*m^u-10*a^u-70*m2
- z^4+1
- 125+a^3
- 49-x^2
- Общий знаменатель:
- (s^2-3*s/9*s^2-1*3*s^2+s/s^3+27-s+3/3*s^2-s)/4/s^2+3*s-15*s+6/4-12*s
- ((7*sqrt(x)-5)/sqrt(x))+(5*sqrt(x)/x)+(3*x-4)
- (u^2-2*u+4)/(4*u^2-1)*(2*u^2+4)/(u^3+8)
- t/(t+3)^3-3/(t+3)^3
- Умножение столбиком:
- 75*12
- 80*11
- 419*217
- 28*34
- Деление столбиком:
- 983/3
- 467/2
- 964/4
- 522/6
- Раскрыть скобки в:
- (2*b+1)*(4*b-2*b+1)
- (z^9)^4*z*(z^5)^7
- n+1^(n+1)
- 2*(x+6)^2-(20*x+70)
- Разложение числа на простые множители:
- 1001
- 31024
- 388
- 4860
- Производная:
- 1/3
- График функции y =:
- 1/3
- Интеграл d{x}:
-
1/3
-
Идентичные выражения
- один /(один +tan(a)^ два)+ один /(один +cot(a)^ два) если a= один / три
- 1 делить на (1 плюс тангенс от (a) в квадрате ) плюс 1 делить на (1 плюс котангенс от (a) в квадрате ) если a равно 1 делить на 3
- один делить на (один плюс тангенс от (a) в степени два) плюс один делить на (один плюс котангенс от (a) в степени два) если a равно один делить на три
- 1/(1+tan(a)2)+1/(1+cot(a)2) если a=1/3
- 1/1+tana2+1/1+cota2 если a=1/3
- 1/(1+tan(a)²)+1/(1+cot(a)²) если a=1/3
- 1/(1+tan(a) в степени 2)+1/(1+cot(a) в степени 2) если a=1/3
- 1/1+tana^2+1/1+cota^2 если a=1/3
- 1/(1+tan(a)^2)+1/(1+cot(a)^2) при a=1/3
- 1 разделить на (1+tan(a)^2)+1 разделить на (1+cot(a)^2) если a=1 разделить на 3
-
Похожие выражения
- 1/(1+tan(a)^2)+1/(1-cot(a)^2) если a=1/3
- 1/(1+tan(a)^2)-1/(1+cot(a)^2) если a=1/3
- 1/(1-tan(a)^2)+1/(1+cot(a)^2) если a=1/3
1/(1+tan(a)^2)+1/(1+cot(a)^2) если a=1/3
Решение
Вы ввели
[src]
1 1
1*----------- + 1*-----------
2 2
1 + tan (a) 1 + cot (a)
$$1 \cdot \frac{1}{\cot^{2}{\left(a \right)} + 1} + 1 \cdot \frac{1}{\tan^{2}{\left(a \right)} + 1}$$
1/(1 + tan(a)^2) + 1/(1 + cot(a)^2)
Собрать выражение
[src]
1 1 ------- + ------- 2 2 csc (a) sec (a)
$$\frac{1}{\sec^{2}{\left(a \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$
1 1
----------- + -----------
2 2
1 + cot (a) 1 + tan (a)
$$\frac{1}{\cot^{2}{\left(a \right)} + 1} + \frac{1}{\tan^{2}{\left(a \right)} + 1}$$
1/(1 + cot(a)^2) + 1/(1 + tan(a)^2)
Общий знаменатель
[src]
2 2
2 + cot (a) + tan (a)
---------------------------------------
2 2 2 2
1 + cot (a) + tan (a) + cot (a)*tan (a)
$$\frac{\tan^{2}{\left(a \right)} + \cot^{2}{\left(a \right)} + 2}{\tan^{2}{\left(a \right)} \cot^{2}{\left(a \right)} + \tan^{2}{\left(a \right)} + \cot^{2}{\left(a \right)} + 1}$$
(2 + cot(a)^2 + tan(a)^2)/(1 + cot(a)^2 + tan(a)^2 + cot(a)^2*tan(a)^2)
Численный ответ
[src]
1/(1.0 + cot(a)^2) + 1/(1.0 + tan(a)^2)
1/(1.0 + cot(a)^2) + 1/(1.0 + tan(a)^2)
Объединение рациональных выражений
[src]
2 2 2 + cot (a) + tan (a) --------------------------- / 2 \ / 2 \ \1 + cot (a)/*\1 + tan (a)/
$$\frac{\tan^{2}{\left(a \right)} + \cot^{2}{\left(a \right)} + 2}{\left(\tan^{2}{\left(a \right)} + 1\right) \left(\cot^{2}{\left(a \right)} + 1\right)}$$
(2 + cot(a)^2 + tan(a)^2)/((1 + cot(a)^2)*(1 + tan(a)^2))
Комбинаторика
[src]
2 2 2 + cot (a) + tan (a) --------------------------- / 2 \ / 2 \ \1 + cot (a)/*\1 + tan (a)/
$$\frac{\tan^{2}{\left(a \right)} + \cot^{2}{\left(a \right)} + 2}{\left(\tan^{2}{\left(a \right)} + 1\right) \left(\cot^{2}{\left(a \right)} + 1\right)}$$
(2 + cot(a)^2 + tan(a)^2)/((1 + cot(a)^2)*(1 + tan(a)^2))
Степени
[src]
1 1
----------- + -----------
2 2
1 + cot (a) 1 + tan (a)
$$\frac{1}{\cot^{2}{\left(a \right)} + 1} + \frac{1}{\tan^{2}{\left(a \right)} + 1}$$
1 1
----------- + ---------------------
2 2
1 + cot (a) / I*a -I*a\
\- e + e /
1 - -----------------
2
/ I*a -I*a\
\e + e /
$$\frac{1}{\cot^{2}{\left(a \right)} + 1} + \frac{1}{- \frac{\left(- e^{i a} + e^{- i a}\right)^{2}}{\left(e^{i a} + e^{- i a}\right)^{2}} + 1}$$
1/(1 + cot(a)^2) + 1/(1 - (-exp(i*a) + exp(-i*a))^2/(exp(i*a) + exp(-i*a))^2)
Рациональный знаменатель
[src]
1 1
----------- + -----------
2 2
1 + cot (a) 1 + tan (a)
$$\frac{1}{\cot^{2}{\left(a \right)} + 1} + \frac{1}{\tan^{2}{\left(a \right)} + 1}$$
2 2 2 + cot (a) + tan (a) --------------------------- / 2 \ / 2 \ \1 + cot (a)/*\1 + tan (a)/
$$\frac{\tan^{2}{\left(a \right)} + \cot^{2}{\left(a \right)} + 2}{\left(\tan^{2}{\left(a \right)} + 1\right) \left(\cot^{2}{\left(a \right)} + 1\right)}$$
(2 + cot(a)^2 + tan(a)^2)/((1 + cot(a)^2)*(1 + tan(a)^2))
Тригонометрическая часть
[src]
1
$$1$$
1 1
----------- + -----------
2 2
1 + cot (a) 1 + tan (a)
$$\frac{1}{\cot^{2}{\left(a \right)} + 1} + \frac{1}{\tan^{2}{\left(a \right)} + 1}$$
1 1
----------- + -----------
1 2
1 + ------- 1 + cot (a)
2
cot (a)
$$\frac{1}{\cot^{2}{\left(a \right)} + 1} + \frac{1}{1 + \frac{1}{\cot^{2}{\left(a \right)}}}$$
1 1
----------- + -----------
1 2
1 + ------- 1 + tan (a)
2
tan (a)
$$\frac{1}{\tan^{2}{\left(a \right)} + 1} + \frac{1}{1 + \frac{1}{\tan^{2}{\left(a \right)}}}$$
2 4/a\ 2/a\
cos (a) - 4*cos |-| + 4*cos |-|
\2/ \2/
$$- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \cos^{2}{\left(a \right)}$$
1 1
----------- + -----------
2 2
sec (a) csc (a)
1 + ------- 1 + -------
2 2
csc (a) sec (a)
$$\frac{1}{\frac{\csc^{2}{\left(a \right)}}{\sec^{2}{\left(a \right)}} + 1} + \frac{1}{1 + \frac{\sec^{2}{\left(a \right)}}{\csc^{2}{\left(a \right)}}}$$
1 1
----------- + -----------
2 2
sin (a) cos (a)
1 + ------- 1 + -------
2 2
cos (a) sin (a)
$$\frac{1}{\frac{\sin^{2}{\left(a \right)}}{\cos^{2}{\left(a \right)}} + 1} + \frac{1}{1 + \frac{\cos^{2}{\left(a \right)}}{\sin^{2}{\left(a \right)}}}$$
1 1
--------------- + ---------------
2 4
4*csc (2*a) csc (a)
1 + ----------- 1 + -----------
4 2
csc (a) 4*csc (2*a)
$$\frac{1}{\frac{\csc^{4}{\left(a \right)}}{4 \csc^{2}{\left(2 a \right)}} + 1} + \frac{1}{1 + \frac{4 \csc^{2}{\left(2 a \right)}}{\csc^{4}{\left(a \right)}}}$$
1 1
------------- + -------------
4 2
4*sin (a) sin (2*a)
1 + --------- 1 + ---------
2 4
sin (2*a) 4*sin (a)
$$\frac{1}{\frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1} + \frac{1}{1 + \frac{\sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}}$$
1 1
---------------- + ----------------
2/ pi\ 2
sec |a - --| sec (a)
\ 2 / 1 + ------------
1 + ------------ 2/ pi\
2 sec |a - --|
sec (a) \ 2 /
$$\frac{1}{\frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1} + \frac{1}{1 + \frac{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}}}$$
1 1
---------------- + ----------------
2/ pi\ 2
sin |a + --| sin (a)
\ 2 / 1 + ------------
1 + ------------ 2/ pi\
2 sin |a + --|
sin (a) \ 2 /
$$\frac{1}{\frac{\sin^{2}{\left(a \right)}}{\sin^{2}{\left(a + \frac{\pi}{2} \right)}} + 1} + \frac{1}{1 + \frac{\sin^{2}{\left(a + \frac{\pi}{2} \right)}}{\sin^{2}{\left(a \right)}}}$$
1 1
---------------- + ----------------
2/ pi\ 2
cos |a - --| cos (a)
\ 2 / 1 + ------------
1 + ------------ 2/ pi\
2 cos |a - --|
cos (a) \ 2 /
$$\frac{1}{\frac{\cos^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}} + 1} + \frac{1}{1 + \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}}$$
1 1
---------------- + ----------------
2/pi \ 2
sec |-- - a| sec (a)
\2 / 1 + ------------
1 + ------------ 2/pi \
2 sec |-- - a|
sec (a) \2 /
$$\frac{1}{\frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(- a + \frac{\pi}{2} \right)}} + 1} + \frac{1}{1 + \frac{\sec^{2}{\left(- a + \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}}}$$
1 1
---------------- + ----------------
2/pi \ 2
csc |-- - a| csc (a)
\2 / 1 + ------------
1 + ------------ 2/pi \
2 csc |-- - a|
csc (a) \2 /
$$\frac{1}{\frac{\csc^{2}{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + 1} + \frac{1}{1 + \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}}$$
1 1
---------------- + ----------------
2/pi \ 2
csc |-- - a| csc (pi - a)
\2 / 1 + ------------
1 + ------------ 2/pi \
2 csc |-- - a|
csc (pi - a) \2 /
$$\frac{1}{\frac{\csc^{2}{\left(- a + \pi \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + 1} + \frac{1}{1 + \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(- a + \pi \right)}}}$$
1 1
------------------ + ------------------
4/ pi\ 2/ pi\
4*cos |a - --| cos |2*a - --|
\ 2 / \ 2 /
1 + -------------- 1 + --------------
2/ pi\ 4/ pi\
cos |2*a - --| 4*cos |a - --|
\ 2 / \ 2 /
$$\frac{1}{\frac{4 \cos^{4}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}} + 1} + \frac{1}{1 + \frac{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}}{4 \cos^{4}{\left(a - \frac{\pi}{2} \right)}}}$$
1 1
-------------------- + --------------------
2/ pi\ 4/ pi\
4*sec |2*a - --| sec |a - --|
\ 2 / \ 2 /
1 + ---------------- 1 + ----------------
4/ pi\ 2/ pi\
sec |a - --| 4*sec |2*a - --|
\ 2 / \ 2 /
$$\frac{1}{\frac{\sec^{4}{\left(a - \frac{\pi}{2} \right)}}{4 \sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} + 1} + \frac{1}{1 + \frac{4 \sec^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\sec^{4}{\left(a - \frac{\pi}{2} \right)}}}$$
1 2
------------------------------------------ + sin (a)
1 - cos(2*a)
1 + --------------------------------------
2 2
/ /a\\ / /a\\ 4/a\
2*|1 + tan|-|| *|-1 + tan|-|| *cos |-|
\ \2// \ \2// \2/
$$\sin^{2}{\left(a \right)} + \frac{1}{1 + \frac{- \cos{\left(2 a \right)} + 1}{2 \left(\tan{\left(\frac{a}{2} \right)} - 1\right)^{2} \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{2} \cos^{4}{\left(\frac{a}{2} \right)}}}$$
1 1
------------------ + ------------------
2/a\ 2
4*tan |-| / 2/a\\
\2/ |1 - tan |-||
1 + -------------- \ \2//
2 1 + --------------
/ 2/a\\ 2/a\
|1 - tan |-|| 4*tan |-|
\ \2// \2/
$$\frac{1}{\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{4 \tan^{2}{\left(\frac{a}{2} \right)}} + 1} + \frac{1}{1 + \frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}}$$
1 1
----------------------------- + -----------------------------
2 4
/ 2 \ 4/a\ / 2/a\\ 2
16*\1 + tan (a)/ *tan |-| |1 + tan |-|| *tan (a)
\2/ \ \2//
1 + ------------------------- 1 + -------------------------
4 2
/ 2/a\\ 2 / 2 \ 4/a\
|1 + tan |-|| *tan (a) 16*\1 + tan (a)/ *tan |-|
\ \2// \2/
$$\frac{1}{\frac{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{4} \tan^{2}{\left(a \right)}}{16 \left(\tan^{2}{\left(a \right)} + 1\right)^{2} \tan^{4}{\left(\frac{a}{2} \right)}} + 1} + \frac{1}{1 + \frac{16 \left(\tan^{2}{\left(a \right)} + 1\right)^{2} \tan^{4}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{4} \tan^{2}{\left(a \right)}}}$$
1 1
------------------------------- + -------------------------------
2 2
/ 2/a pi\\ 2/a\ / 2/a\\ 2/a pi\
|1 + tan |- + --|| *cot |-| |1 + cot |-|| *tan |- + --|
\ \2 4 // \2/ \ \2// \2 4 /
1 + --------------------------- 1 + ---------------------------
2 2
/ 2/a\\ 2/a pi\ / 2/a pi\\ 2/a\
|1 + cot |-|| *tan |- + --| |1 + tan |- + --|| *cot |-|
\ \2// \2 4 / \ \2 4 // \2/
$$\frac{1}{\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1} + \frac{1}{1 + \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \cot^{2}{\left(\frac{a}{2} \right)}}}$$
1 1
--------------------------------------- + ---------------------------------------
2 2 2 2
/ 2/a pi\\ / 2/a\\ / 2/a\\ / 2/a pi\\
|1 + tan |- + --|| *|-1 + cot |-|| |1 + cot |-|| *|-1 + tan |- + --||
\ \2 4 // \ \2// \ \2// \ \2 4 //
1 + ----------------------------------- 1 + -----------------------------------
2 2 2 2
/ 2/a\\ / 2/a pi\\ / 2/a pi\\ / 2/a\\
|1 + cot |-|| *|-1 + tan |- + --|| |1 + tan |- + --|| *|-1 + cot |-||
\ \2// \ \2 4 // \ \2 4 // \ \2//
$$\frac{1}{\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}} + 1} + \frac{1}{1 + \frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}}$$
1 1
-------------------------------------- + --------------------------------------
2 2 2 2
/ 2/a\\ / 2/a pi\\ / 2/a pi\\ / 2/a\\
|1 + tan |-|| *|1 - cot |- + --|| |1 + cot |- + --|| *|1 - tan |-||
\ \2// \ \2 4 // \ \2 4 // \ \2//
1 + ---------------------------------- 1 + ----------------------------------
2 2 2 2
/ 2/a pi\\ / 2/a\\ / 2/a\\ / 2/a pi\\
|1 + cot |- + --|| *|1 - tan |-|| |1 + tan |-|| *|1 - cot |- + --||
\ \2 4 // \ \2// \ \2// \ \2 4 //
$$\frac{1}{\frac{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} + 1} + \frac{1}{1 + \frac{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(- \tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}$$
1 1
--------------------------------------------------------------------------------- + -----------------------------------------------------------------------
// 0 for a mod pi = 0\ // zoo for 2*a mod pi = 0\ // zoo for a mod pi = 0\
|| | || | || |
1 + 4*|< 4/a\ 8/a\ |*|< 2 | // 0 for 2*a mod pi = 0\ || 4/a\ |
||16*cot |-|*sin |-| otherwise | ||------------ otherwise | || | || tan |-| |
\\ \2/ \2/ / \\1 - cos(4*a) / |<1 - cos(4*a) |*|< \2/ |
||------------ otherwise | ||---------- otherwise |
\\ 2 / || 8/a\ |
||16*sin |-| |
\\ \2/ /
1 + -------------------------------------------------------------------
4
$$\left(\frac{1}{\left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{- \cos{\left(4 a \right)} + 1}{2} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: a \bmod \pi = 0 \\\frac{\tan^{4}{\left(\frac{a}{2} \right)}}{16 \sin^{8}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)}{4}\right) + 1}\right) + \left(\frac{1}{\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\16 \sin^{8}{\left(\frac{a}{2} \right)} \cot^{4}{\left(\frac{a}{2} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: 2 a \bmod \pi = 0 \\\frac{2}{- \cos{\left(4 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + 1}\right)$$
1 1
------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------
// / 3*pi\ \ // / 3*pi\ \
|| 1 for |a + ----| mod 2*pi = 0| // 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| \ 2 / | || | || \ 2 / |
|| | 1 + |< 2 |*|< |
// 1 for a mod 2*pi = 0\ || 1 | ||------------ otherwise | || 4/a\ 2/a\ |
|| | ||-1 + ------- | \\1 + cos(2*a) / ||- 4*cos |-| + 4*cos |-| otherwise |
1 + |< 2 |*|< 2/a\ | \\ \2/ \2/ /
||cos (a) otherwise | || sin |-| |
\\ / || \2/ |
||------------ otherwise |
|| 4/a\ |
|| 4*cos |-| |
\\ \2/ /
$$\left(\frac{1}{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\sin^{2}{\left(\frac{a}{2} \right)}}}{4 \cos^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + 1}\right) + \left(\frac{1}{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{2}{\cos{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + 1}\right)$$
1 1
------------------------------------------------------------------------------- + -----------------------------------------------------------------------------
// 0 for a mod pi = 0\ // zoo for a mod pi = 0\
|| | // zoo for 2*a mod pi = 0\ // 0 for 2*a mod pi = 0\ || |
|| 4/a\ | || | || | || 4 |
|| 16*cot |-| | || 2 | || 2 | ||/ 2/a\\ |
|| \2/ | ||/ 2 \ | || 4*cot (a) | |||1 + cot |-|| |
1 + 4*|<-------------- otherwise |*|<\1 + cot (a)/ | |<-------------- otherwise |*|<\ \2// |
|| 4 | ||-------------- otherwise | || 2 | ||-------------- otherwise |
||/ 2/a\\ | || 2 | ||/ 2 \ | || 4/a\ |
|||1 + cot |-|| | || 4*cot (a) | ||\1 + cot (a)/ | || 16*cot |-| |
||\ \2// | \\ / \\ / || \2/ |
\\ / \\ /
1 + -------------------------------------------------------------------------
4
$$\left(\frac{1}{\left(\frac{\left(\begin{cases} 0 & \text{for}\: 2 a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(a \right)}}{\left(\cot^{2}{\left(a \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: a \bmod \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{4}}{16 \cot^{4}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right)}{4}\right) + 1}\right) + \left(\frac{1}{\left(4 \left(\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{16 \cot^{4}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{4}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: 2 a \bmod \pi = 0 \\\frac{\left(\cot^{2}{\left(a \right)} + 1\right)^{2}}{4 \cot^{2}{\left(a \right)}} & \text{otherwise} \end{cases}\right)\right) + 1}\right)$$
1 1
----------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------
// / 3*pi\ \ // / 3*pi\ \
// 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0| // 1 for a mod 2*pi = 0\ || 1 for |a + ----| mod 2*pi = 0|
|| | || \ 2 / | || | || \ 2 / |
|| 2 | || | || 2 | || |
||/ 2/a\\ | || 2 | || / 2/a\\ | || 2 |
|||-1 + cot |-|| | ||/ 2/a pi\\ | || |1 + cot |-|| | ||/ 2/a pi\\ |
1 + |<\ \2// |*|<|1 + tan |- + --|| | 1 + |< \ \2// |*|<|-1 + tan |- + --|| |
||--------------- otherwise | ||\ \2 4 // | ||--------------- otherwise | ||\ \2 4 // |
|| 2 | ||-------------------- otherwise | || 2 | ||-------------------- otherwise |
|| / 2/a\\ | || 2 | ||/ 2/a\\ | || 2 |
|| |1 + cot |-|| | ||/ 2/a pi\\ | |||-1 + cot |-|| | ||/ 2/a pi\\ |
\\ \ \2// / |||-1 + tan |- + --|| | \\\ \2// / |||1 + tan |- + --|| |
\\\ \2 4 // / \\\ \2 4 // /
$$\left(\frac{1}{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1}\right) + \left(\frac{1}{\left(\left(\begin{cases} 1 & \text{for}\: a \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right) + 1}\right)$$
1/(1 + Piecewise((1, Mod(a = 2*pi, 0)), ((-1 + cot(a/2)^2)^2/(1 + cot(a/2)^2)^2, True))*Piecewise((1, Mod(a + 3*pi/2 = 2*pi, 0)), ((1 + tan(a/2 + pi/4)^2)^2/(-1 + tan(a/2 + pi/4)^2)^2, True))) + 1/(1 + Piecewise((1, Mod(a = 2*pi, 0)), ((1 + cot(a/2)^2)^2/(-1 + cot(a/2)^2)^2, True))*Piecewise((1, Mod(a + 3*pi/2 = 2*pi, 0)), ((-1 + tan(a/2 + pi/4)^2)^2/(1 + tan(a/2 + pi/4)^2)^2, True)))