Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
((sin((3*pi)/2-a)^(2))+(cos((3*pi)/2-a)^(2)))/((1/tan(a)^2)*(pi-a)*tan(pi-a)^(2))
¿Cómo vas a descomponer esta ((sin((3*pi)/2-a)^(2))+(cos((3*pi)/2-a)^(2)))/((1/tan(a)^2)*(pi-a)*tan(pi-a)^(2)) expresión en fracciones?
Solución
Ha introducido
[src]
2/3*pi \ 2/3*pi \
sin |---- - a| + cos |---- - a|
\ 2 / \ 2 /
-------------------------------
pi - a 2
-------*tan (pi - a)
2
tan (a)
$$\frac{\sin^{2}{\left(- a + \frac{3 \pi}{2} \right)} + \cos^{2}{\left(- a + \frac{3 \pi}{2} \right)}}{\frac{\pi - a}{\tan^{2}{\left(a \right)}} \tan^{2}{\left(\pi - a \right)}}$$
(sin((3*pi)/2 - a)^2 + cos((3*pi)/2 - a)^2)/((((pi - a)/tan(a)^2)*tan(pi - a)^2))
Respuesta numérica
[src]
tan(a)^2*(cos((3*pi)/2 - a)^2 + sin((3*pi)/2 - a)^2)/((3.14159265358979 - a)*tan(pi - a)^2)
tan(a)^2*(cos((3*pi)/2 - a)^2 + sin((3*pi)/2 - a)^2)/((3.14159265358979 - a)*tan(pi - a)^2)
Combinatoria
[src]
/ 2 2 \
-\cos (a) + sin (a)/
---------------------
a - pi
$$- \frac{\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}}{a - \pi}$$
-(cos(a)^2 + sin(a)^2)/(a - pi)
Unión de expresiones racionales
[src]
2/-2*a + 3*pi\ 2/-2*a + 3*pi\
cos |-----------| + sin |-----------|
\ 2 / \ 2 /
-------------------------------------
pi - a
$$\frac{\sin^{2}{\left(\frac{- 2 a + 3 \pi}{2} \right)} + \cos^{2}{\left(\frac{- 2 a + 3 \pi}{2} \right)}}{\pi - a}$$
(cos((-2*a + 3*pi)/2)^2 + sin((-2*a + 3*pi)/2)^2)/(pi - a)
Denominador común
[src]
/ 2 2 2 2 \
-\cos (a)*tan (a) + sin (a)*tan (a)/
-------------------------------------
2 2
a*tan (pi - a) - pi*tan (pi - a)
$$- \frac{\sin^{2}{\left(a \right)} \tan^{2}{\left(a \right)} + \cos^{2}{\left(a \right)} \tan^{2}{\left(a \right)}}{a \tan^{2}{\left(\pi - a \right)} - \pi \tan^{2}{\left(\pi - a \right)}}$$
-(cos(a)^2*tan(a)^2 + sin(a)^2*tan(a)^2)/(a*tan(pi - a)^2 - pi*tan(pi - a)^2)
Compilar la expresión
[src]
2 / 2/3*pi \ 2/3*pi \\
tan (a)*|cos |---- - a| + sin |---- - a||
\ \ 2 / \ 2 //
-----------------------------------------
2
(pi - a)*tan (pi - a)
$$\frac{\left(\sin^{2}{\left(- a + \frac{3 \pi}{2} \right)} + \cos^{2}{\left(- a + \frac{3 \pi}{2} \right)}\right) \tan^{2}{\left(a \right)}}{\left(\pi - a\right) \tan^{2}{\left(\pi - a \right)}}$$
tan(a)^2*(cos((3*pi)/2 - a)^2 + sin((3*pi)/2 - a)^2)/((pi - a)*tan(pi - a)^2)
Denominador racional
[src]
2 2
- cos (a) - sin (a)
-------------------
a - pi
$$\frac{- \sin^{2}{\left(a \right)} - \cos^{2}{\left(a \right)}}{a - \pi}$$
(-cos(a)^2 - sin(a)^2)/(a - pi)
Potencias
[src]
2 2
cos (a) + sin (a)
-----------------
pi - a
$$\frac{\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}}{\pi - a}$$
/ 2 2\
|/ / 3*pi\ / 3*pi\\ / / 3*pi\ / 3*pi\\ |
|| I*|a - ----| I*|-a + ----|| | I*|a - ----| I*|-a + ----|| |
2 2 || \ 2 / \ 2 /| | \ 2 / \ 2 /| |
/ I*a -I*a\ / I*(pi - a) I*(a - pi)\ ||e e | \- e + e / |
\- e + e / *\e + e / *||------------- + --------------| - -----------------------------------|
\\ 2 2 / 4 /
------------------------------------------------------------------------------------------------------------------------
2 2
/ I*(pi - a) I*(a - pi)\ / I*a -I*a\
(pi - a)*\- e + e / *\e + e /
$$\frac{\left(\left(\frac{e^{i \left(- a + \frac{3 \pi}{2}\right)}}{2} + \frac{e^{i \left(a - \frac{3 \pi}{2}\right)}}{2}\right)^{2} - \frac{\left(e^{i \left(- a + \frac{3 \pi}{2}\right)} - e^{i \left(a - \frac{3 \pi}{2}\right)}\right)^{2}}{4}\right) \left(- e^{i a} + e^{- i a}\right)^{2} \left(e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right)^{2}}{\left(\pi - a\right) \left(e^{i a} + e^{- i a}\right)^{2} \left(- e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right)^{2}}$$
(-exp(i*a) + exp(-i*a))^2*(exp(i*(pi - a)) + exp(i*(a - pi)))^2*((exp(i*(a - 3*pi/2))/2 + exp(i*(-a + 3*pi/2))/2)^2 - (-exp(i*(a - 3*pi/2)) + exp(i*(-a + 3*pi/2)))^2/4)/((pi - a)*(-exp(i*(pi - a)) + exp(i*(a - pi)))^2*(exp(i*a) + exp(-i*a))^2)
Parte trigonométrica
[src]
2/a pi\
4*cos |- - --|
4/a\ 2/a\ \2 4 /
- 4*cos |-| + 4*cos |-| + --------------------------------
\2/ \2/ 2
/ 2/a pi\\
| cos |- - --||
| \2 4 /| 2/a pi\
|1 + ------------| *cos |- + --|
| 2/a pi\| \2 4 /
| cos |- + --||
\ \2 4 //
----------------------------------------------------------
pi - a
$$\frac{- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \frac{4 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)^{2} \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}}{\pi - a}$$
2
/ 1 \ 4/a\
|1 + -----------| *sec |-|
| / pi\| \2/
| sec|a - --||
\ \ 2 //
---------------------------
4
/ /a\ \
| sec|-| |
| \2/ |
|1 + -----------| *(pi - a)
| /a pi\|
| sec|- - --||
\ \2 2 //
$$\frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right)^{2} \sec^{4}{\left(\frac{a}{2} \right)}}{\left(\pi - a\right) \left(\frac{\sec{\left(\frac{a}{2} \right)}}{\sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right)^{4}}$$
2
/ 2/a pi\\ 2/a pi\
|1 - tan |- + --|| 4*tan |- + --|
\ \2 4 // \2 4 /
------------------- + -------------------
2 2
/ 2/a pi\\ / 2/a pi\\
|1 + tan |- + --|| |1 + tan |- + --||
\ \2 4 // \ \2 4 //
-----------------------------------------
pi - a
$$\frac{\frac{\left(1 - \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a}$$
2/a pi\
4*sec |- + --|
4 4 \2 4 /
- ------- + ------- + --------------------------------
4/a\ 2/a\ 2
sec |-| sec |-| / 2/a pi\\
\2/ \2/ | sec |- + --||
| \2 4 /| 2/a pi\
|1 + ------------| *sec |- - --|
| 2/a pi\| \2 4 /
| sec |- - --||
\ \2 4 //
------------------------------------------------------
pi - a
$$\frac{\frac{4}{\sec^{2}{\left(\frac{a}{2} \right)}} - \frac{4}{\sec^{4}{\left(\frac{a}{2} \right)}} + \frac{4 \sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}\right)^{2} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}}{\pi - a}$$
4 2
/ 2/a\\ / 2/a\\
4*|-1 + cot |-|| 4*|-1 + cot |-||
\ \4// \ \4// 4
- ----------------- + ----------------- + --------------------------------
4 2 2
/ 2/a\\ / 2/a\\ / 1 \ 2/a pi\
|1 + cot |-|| |1 + cot |-|| |1 + ------------| *cot |- + --|
\ \4// \ \4// | 2/a pi\| \2 4 /
| cot |- + --||
\ \2 4 //
--------------------------------------------------------------------------
pi - a
$$\frac{- \frac{4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}} + \frac{4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}} + \frac{4}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right)^{2} \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}}{\pi - a}$$
2
/ /a\ \
4 | 2*tan|-| |
/ 2/a\\ | \2/ |
|1 + tan |-|| *|1 + -----------|
\ \4// | 2/a\|
| 1 + tan |-||
\ \2//
-------------------------------------
4 4
/ 2/a\\ / /a\\
|1 - tan |-|| *|1 + tan|-|| *(pi - a)
\ \4// \ \2//
$$\frac{\left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right)^{2} \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}}{\left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4}}$$
2
/ / pi\\
|1 + cos|a - --||
\ \ 2 //
-----------------------------------
4
/ /a pi\\
| cos|- - --||
| \2 2 /| 4/a\
|1 + -----------| *(pi - a)*cos |-|
| /a\ | \2/
| cos|-| |
\ \2/ /
$$\frac{\left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right)^{2}}{\left(1 + \frac{\cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos{\left(\frac{a}{2} \right)}}\right)^{4} \left(\pi - a\right) \cos^{4}{\left(\frac{a}{2} \right)}}$$
2
/ 2/a pi\\ 2/a pi\
|-1 + cot |- + --|| 4*cot |- + --|
\ \2 4 // \2 4 /
-------------------- + -------------------
2 2
/ 2/a pi\\ / 2/a pi\\
|1 + cot |- + --|| |1 + cot |- + --||
\ \2 4 // \ \2 4 //
------------------------------------------
pi - a
$$\frac{\frac{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} + \frac{4 \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a}$$
1 1
------- + ------------
2 2
csc (a) sec (pi - a)
----------------------
pi - a
$$\frac{\frac{1}{\sec^{2}{\left(\pi - a \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}}{\pi - a}$$
1 1
------- + ------------
2 2/pi \
sec (a) sec |-- - a|
\2 /
----------------------
pi - a
$$\frac{\frac{1}{\sec^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\sec^{2}{\left(a \right)}}}{\pi - a}$$
2 2/ pi\
sin (a) + sin |a + --|
\ 2 /
----------------------
pi - a
$$\frac{\sin^{2}{\left(a \right)} + \sin^{2}{\left(a + \frac{\pi}{2} \right)}}{\pi - a}$$
2/ a pi\
4*csc |- - + --|
4 4 \ 2 4 /
- ------------ + ------------ + ----------------------------------
4/pi a\ 2/pi a\ 2
csc |-- - -| csc |-- - -| / 2/ a pi\\
\2 2/ \2 2/ | csc |- - + --||
| \ 2 4 /| 2/a pi\
|1 + --------------| *csc |- + --|
| 2/a pi\ | \2 4 /
| csc |- + --| |
\ \2 4 / /
------------------------------------------------------------------
pi - a
$$\frac{\frac{4}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - \frac{4}{\csc^{4}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + \frac{4 \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} + 1\right)^{2} \csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}}{\pi - a}$$
2/a pi\
4 4*tan |- + --|
/ 2/a\\ 8/a\ \2 4 /
2*(1 + cos(a)) - 4*|-1 + cot |-|| *sin |-| + -------------------
\ \4// \4/ 2
/ 2/a pi\\
|1 + tan |- + --||
\ \2 4 //
----------------------------------------------------------------
pi - a
$$\frac{2 \left(\cos{\left(a \right)} + 1\right) - 4 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{a}{4} \right)} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a}$$
2
/ /a\ \
4 | 2*cot|-| |
/ 2/a\\ | \2/ |
|1 + cot |-|| *|1 + -----------|
\ \4// | 2/a\|
| 1 + cot |-||
\ \2//
--------------------------------------
4 4
/ 1 \ / 2/a\\
|1 + ------| *|-1 + cot |-|| *(pi - a)
| /a\| \ \4//
| cot|-||
\ \2//
$$\frac{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right)^{2} \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}}{\left(1 + \frac{1}{\cot{\left(\frac{a}{2} \right)}}\right)^{4} \left(\pi - a\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4}}$$
2
(1 + sin(a))
--------------------------------------
4
/ 2/a\\
| 2*sin |-||
| \2/| 4/pi a\
|1 + ---------| *(pi - a)*sin |-- + -|
\ sin(a) / \2 2/
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\pi - a\right) \left(\frac{2 \sin^{2}{\left(\frac{a}{2} \right)}}{\sin{\left(a \right)}} + 1\right)^{4} \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}}$$
2 4/a\ 2/a\
cos (a) - 4*cos |-| + 4*cos |-|
\2/ \2/
-------------------------------
pi - a
$$\frac{- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \cos^{2}{\left(a \right)}}{\pi - a}$$
2
/ 1 \ 4/pi a\
|1 + ------| *csc |-- - -|
\ csc(a)/ \2 2/
---------------------------
4
/ /pi a\\
| csc|-- - -||
| \2 2/|
|1 + -----------| *(pi - a)
| /a\ |
| csc|-| |
\ \2/ /
$$\frac{\left(1 + \frac{1}{\csc{\left(a \right)}}\right)^{2} \csc^{4}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc{\left(\frac{a}{2} \right)}}\right)^{4} \left(\pi - a\right)}$$
2/a pi\
4*tan |- + --|
4/a\ 2/a\ \2 4 /
- 4*cos |-| + 4*cos |-| + -------------------
\2/ \2/ 2
/ 2/a pi\\
|1 + tan |- + --||
\ \2 4 //
---------------------------------------------
pi - a
$$\frac{- 4 \cos^{4}{\left(\frac{a}{2} \right)} + 4 \cos^{2}{\left(\frac{a}{2} \right)} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a}$$
1 1
------- + -------
2 2
csc (a) sec (a)
-----------------
pi - a
$$\frac{\frac{1}{\sec^{2}{\left(a \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}}{\pi - a}$$
2
(1 + sin(a))
------------------------------
4
/ /a\\ 4/a\
|1 + tan|-|| *(pi - a)*cos |-|
\ \2// \2/
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4} \cos^{4}{\left(\frac{a}{2} \right)}}$$
2
(1 + sin(a))
----------------------------------------------
4 4
/ /a\\ / 2/a\\ 8/a\
|1 + tan|-|| *|-1 + cot |-|| *(pi - a)*sin |-|
\ \2// \ \4// \4/
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{a}{4} \right)}}$$
2 2
cos (a) + sin (-a + 2*pi)
-------------------------
pi - a
$$\frac{\sin^{2}{\left(- a + 2 \pi \right)} + \cos^{2}{\left(a \right)}}{\pi - a}$$
2
(1 + sin(a))
---------------------------------------
4
/ 1 1 \ 4/a\
(pi - a)*|1 + ------ - ------| *cos |-|
\ sin(a) tan(a)/ \2/
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(\pi - a\right) \left(1 - \frac{1}{\tan{\left(a \right)}} + \frac{1}{\sin{\left(a \right)}}\right)^{4} \cos^{4}{\left(\frac{a}{2} \right)}}$$
2/a pi\
4 4*tan |- + --|
/ 2/a\\ 8/a\ \2 4 /
2*(1 + cos(a)) - 4*|1 - tan |-|| *cos |-| + -------------------
\ \4// \4/ 2
/ 2/a pi\\
|1 + tan |- + --||
\ \2 4 //
---------------------------------------------------------------
pi - a
$$\frac{- 4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \cos^{8}{\left(\frac{a}{4} \right)} + 2 \left(\cos{\left(a \right)} + 1\right) + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a}$$
1 ------ pi - a
$$\frac{1}{\pi - a}$$
2 2/ pi\
cos (a) + cos |a - --|
\ 2 /
----------------------
pi - a
$$\frac{\cos^{2}{\left(a \right)} + \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\pi - a}$$
2
(1 + sin(a))
---------------------------------------------
4 4
/ 2/a\\ / /a\\ 8/a\
|1 - tan |-|| *|1 + tan|-|| *(pi - a)*cos |-|
\ \4// \ \2// \4/
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4} \cos^{8}{\left(\frac{a}{4} \right)}}$$
4/a pi\
16*sin |- + --|
4/pi a\ 2/pi a\ \2 4 /
- 4*sin |-- + -| + 4*sin |-- + -| + -----------------------------
\2 2/ \2 2/ 2
/ 4/a pi\\
| 4*sin |- + --||
| \2 4 /| 2
|1 + --------------| *cos (a)
| 2 |
\ cos (a) /
-----------------------------------------------------------------
pi - a
$$\frac{- 4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} + 4 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} + \frac{16 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(a \right)}} + 1\right)^{2} \cos^{2}{\left(a \right)}}}{\pi - a}$$
2/ pi\ / 2 2 \
cos |a - --|*\cos (pi - a) + sin (a)/
\ 2 /
-------------------------------------
2/pi \
(pi - a)*cos |-- - a|
\2 /
$$\frac{\left(\sin^{2}{\left(a \right)} + \cos^{2}{\left(\pi - a \right)}\right) \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\left(\pi - a\right) \cos^{2}{\left(- a + \frac{\pi}{2} \right)}}$$
4 2
/ 2/a\\ / 2/a\\ 2/a pi\
4*|1 - tan |-|| 4*|1 - tan |-|| 4*tan |- + --|
\ \4// \ \4// \2 4 /
- ---------------- + ---------------- + -------------------
4 2 2
/ 2/a\\ / 2/a\\ / 2/a pi\\
|1 + tan |-|| |1 + tan |-|| |1 + tan |- + --||
\ \4// \ \4// \ \2 4 //
-----------------------------------------------------------
pi - a
$$\frac{- \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4}} + \frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}}{\pi - a}$$
2 4/a\
(1 + sin(a)) *sec |-|
\2/
----------------------
4
/ /a\\
|1 + tan|-|| *(pi - a)
\ \2//
$$\frac{\left(\sin{\left(a \right)} + 1\right)^{2} \sec^{4}{\left(\frac{a}{2} \right)}}{\left(\pi - a\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)^{4}}$$
1 1
------- + ------------
2 2/pi \
csc (a) csc |-- - a|
\2 /
----------------------
pi - a
$$\frac{\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}}{\pi - a}$$
(csc(a)^(-2) + csc(pi/2 - a)^(-2))/(pi - a)