Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cot(-a)*sin(6*pi/5-a)*cos(pi-a)*tan(3*pi/(2+a))/(cos(pi-a)^2)
¿Cómo vas a descomponer esta cot(-a)*sin(6*pi/5-a)*cos(pi-a)*tan(3*pi/(2+a))/(cos(pi-a)^2) expresión en fracciones?
Solución
Ha introducido
[src]
/6*pi \ / 3*pi\
cot(-a)*sin|---- - a|*cos(pi - a)*tan|-----|
\ 5 / \2 + a/
--------------------------------------------
2
cos (pi - a)
$$\frac{\sin{\left(- a + \frac{6 \pi}{5} \right)} \cot{\left(- a \right)} \cos{\left(\pi - a \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)}}{\cos^{2}{\left(\pi - a \right)}}$$
(((cot(-a)*sin((6*pi)/5 - a))*cos(pi - a))*tan((3*pi)/(2 + a)))/cos(pi - a)^2
Simplificación general
[src]
/ ______________\
| / ___ |
| ___ \/ 10 - 2*\/ 5 | / 3*pi\
|1 + \/ 5 - -----------------|*tan|-----|
\ tan(a) / \2 + a/
------------------------------------------
4
$$\frac{\left(1 + \sqrt{5} - \frac{\sqrt{10 - 2 \sqrt{5}}}{\tan{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4}$$
(1 + sqrt(5) - sqrt(10 - 2*sqrt(5))/tan(a))*tan(3*pi/(2 + a))/4
Respuesta numérica
[src]
cot(-a)*sin((6*pi)/5 - a)*tan((3*pi)/(2 + a))/cos(pi - a)
cot(-a)*sin((6*pi)/5 - a)*tan((3*pi)/(2 + a))/cos(pi - a)
Denominador racional
[src]
/ 3*pi\ / 3*pi\
-cos|a + ----|*cot(a)*tan|-----|
\ 10 / \2 + a/
---------------------------------
cos(a)
$$- \frac{\cos{\left(a + \frac{3 \pi}{10} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$
-cos(a + 3*pi/10)*cot(a)*tan(3*pi/(2 + a))/cos(a)
Unión de expresiones racionales
[src]
/-5*a + 6*pi\ / 3*pi\
cot(a)*sin|-----------|*tan|-----|
\ 5 / \2 + a/
----------------------------------
cos(a)
$$\frac{\sin{\left(\frac{- 5 a + 6 \pi}{5} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$
cot(a)*sin((-5*a + 6*pi)/5)*tan(3*pi/(2 + a))/cos(a)
Combinatoria
[src]
/ 3*pi\ / 3*pi\
-cos|a + ----|*cot(a)*tan|-----|
\ 10 / \2 + a/
---------------------------------
cos(a)
$$- \frac{\cos{\left(a + \frac{3 \pi}{10} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$
-cos(a + 3*pi/10)*cot(a)*tan(3*pi/(2 + a))/cos(a)
Denominador común
[src]
/ 3*pi\ / 3*pi\
-cos|a + ----|*cot(-a)*tan|-----|
\ 10 / \2 + a/
----------------------------------
cos(pi - a)
$$- \frac{\cos{\left(a + \frac{3 \pi}{10} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(- a \right)}}{\cos{\left(\pi - a \right)}}$$
-cos(a + 3*pi/10)*cot(-a)*tan(3*pi/(2 + a))/cos(pi - a)
Potencias
[src]
/ 3*pi\ / 3*pi\
-cos|a + ----|*cot(a)*tan|-----|
\ 10 / \2 + a/
---------------------------------
cos(a)
$$- \frac{\cos{\left(a + \frac{3 \pi}{10} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)}}{\cos{\left(a \right)}}$$
/ / 6*pi\ / 6*pi\\ / 3*pi*I -3*pi*I\
| I*|a - ----| I*|-a + ----|| | ------ -------|
| \ 5 / \ 5 /| | 2 + a 2 + a |
-\- e + e /*\- e + e /*cot(a)
------------------------------------------------------------------
/ -3*pi*I 3*pi*I\
/ I*(pi - a) I*(a - pi)\ | ------- ------|
|e e | | 2 + a 2 + a |
2*|----------- + -----------|*\e + e /
\ 2 2 /
$$- \frac{\left(e^{i \left(- a + \frac{6 \pi}{5}\right)} - e^{i \left(a - \frac{6 \pi}{5}\right)}\right) \left(- e^{\frac{3 i \pi}{a + 2}} + e^{- \frac{3 i \pi}{a + 2}}\right) \cot{\left(a \right)}}{2 \left(\frac{e^{i \left(\pi - a\right)}}{2} + \frac{e^{i \left(a - \pi\right)}}{2}\right) \left(e^{\frac{3 i \pi}{a + 2}} + e^{- \frac{3 i \pi}{a + 2}}\right)}$$
-(-exp(i*(a - 6*pi/5)) + exp(i*(-a + 6*pi/5)))*(-exp(3*pi*i/(2 + a)) + exp(-3*pi*i/(2 + a)))*cot(a)/(2*(exp(i*(pi - a))/2 + exp(i*(a - pi))/2)*(exp(-3*pi*i/(2 + a)) + exp(3*pi*i/(2 + a))))
Compilar la expresión
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/6*pi \ / 3*pi\
cot(-a)*sin|---- - a|*tan|-----|
\ 5 / \2 + a/
--------------------------------
cos(pi - a)
$$\frac{\sin{\left(- a + \frac{6 \pi}{5} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(- a \right)}}{\cos{\left(\pi - a \right)}}$$
cot(-a)*sin((6*pi)/5 - a)*tan((3*pi)/(2 + a))/cos(pi - a)
Parte trigonométrica
[src]
/ 1 \ / 3*pi\ /a 2*pi\ |1 - ------|*tan|-----|*tan|- + ----| \ cos(a)/ \2 + a/ \2 5 / ------------------------------------- / 2/a 2*pi\\ 2/a\ |1 + tan |- + ----||*sin |-|*tan(a) \ \2 5 // \2/
$$\frac{\left(1 - \frac{1}{\cos{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)}}$$
/ 3*pi\
-csc(a)*sec|-----|
\2 + a/
------------------------
/ 3*pi\ / 3*pi\
csc|-----|*sec|a + ----|
\2 + a/ \ 10 /
$$- \frac{\csc{\left(a \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)}}{\csc{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a + \frac{3 \pi}{10} \right)}}$$
2/a\ / 3*pi\ / 3*pi\
2*sec |-|*cos(a)*sec|-----|*sin|-----|
\2/ \2 + a/ \2 + a/
-----------------------------------------------
/ 2/a\\ /a pi\ /a 2*pi\
|-1 + tan |-||*sec|- - --|*sec|- + ----|*sin(a)
\ \2// \2 10/ \2 5 /
$$\frac{2 \sin{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a \right)} \sec^{2}{\left(\frac{a}{2} \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \sin{\left(a \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{10} \right)} \sec{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}$$
2/ 3*pi\ / 3*pi\
sin |-----|*cos|a + ----|*sin(2*a)
\2 + a/ \ 10 /
----------------------------------
2 / 6*pi\ / 3*pi\
sin (a)*sin|-----|*sin|-a + ----|
\2 + a/ \ 2 /
$$\frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}{\sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \sin{\left(- a + \frac{3 \pi}{2} \right)}}$$
2/a\ / 3*pi\ / pi\
2*sec |-|*sec|-----|*sec|a - --|
\2/ \2 + a/ \ 2 /
----------------------------------------------------------------------
/ 2/a\ \
| sec |-| |
| \2/ | /a pi\ /a 2*pi\ / pi 3*pi\
|-1 + ------------|*sec(a)*sec|- - --|*sec|- + ----|*sec|- -- + -----|
| 2/a pi\| \2 10/ \2 5 / \ 2 2 + a/
| sec |- - --||
\ \2 2 //
$$\frac{2 \sec^{2}{\left(\frac{a}{2} \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{10} \right)} \sec{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}$$
/ 1 1 \ /a pi\ /a 2*pi\ / 3*pi\
4*|- - - --------|*cos(a)*cos|- - --|*cos|- + ----|*sin|-----|
\ 2 2*cos(a)/ \2 10/ \2 5 / \2 + a/
--------------------------------------------------------------
/ 3*pi\
(1 + cos(a))*cos|-----|*sin(a)
\2 + a/
$$\frac{4 \left(- \frac{1}{2} - \frac{1}{2 \cos{\left(a \right)}}\right) \sin{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{10} \right)} \cos{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\cos{\left(a \right)} + 1\right) \sin{\left(a \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)}}$$
/ 2/a\\ / 3*pi\ /a 2*pi\ 2*|1 + cot |-||*tan|-----|*tan|- + ----| \ \2// \2 + a/ \2 5 / ----------------------------------------- / 2/a 2*pi\\ / 2/a\\ |1 + tan |- + ----||*|1 - cot |-||*tan(a) \ \2 5 // \ \2//
$$\frac{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \tan{\left(a \right)}}$$
/ ___________ \
| ___ ___ / ___ | / 3*pi\
\1 + \/ 5 - \/ 2 *\/ 5 - \/ 5 *cot(a)/*tan|-----|
\2 + a/
----------------------------------------------------
4
$$\frac{\left(- \sqrt{2} \sqrt{5 - \sqrt{5}} \cot{\left(a \right)} + 1 + \sqrt{5}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4}$$
/ 7*pi\ / pi 3*pi\
-cos|-a + ----|*cos|- -- + -----|
\ 10 / \ 2 2 + a/
----------------------------------
/ 3*pi\ / pi\
cos|-----|*cos|-a - --|
\2 + a/ \ 2 /
$$- \frac{\cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \cos{\left(- a + \frac{7 \pi}{10} \right)}}{\cos{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(- a - \frac{\pi}{2} \right)}}$$
2
/ _____________ \
| / ___ /a\| 2/a\ / 3*pi\ /a 2*pi\
-4*|-1 + \/ 5 + 2*\/ 5 *tan|-|| *cos |-|*tan|-----|*tan|- + ----|
\ \2// \2/ \2 + a/ \2 5 /
-------------------------------------------------------------------
___
12*sin(a) + 4*\/ 5 *sin(a)
$$- \frac{4 \left(\sqrt{2 \sqrt{5} + 5} \tan{\left(\frac{a}{2} \right)} - 1\right)^{2} \cos^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{4 \sqrt{5} \sin{\left(a \right)} + 12 \sin{\left(a \right)}}$$
2/ 3*pi\ / 4*pi\
-sin |-----|*sin(2*a)*sin|a + ----|
\2 + a/ \ 5 /
------------------------------------
2 / 6*pi\
cos(a)*sin (a)*sin|-----|
\2 + a/
$$- \frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \sin{\left(a + \frac{4 \pi}{5} \right)}}{\sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \cos{\left(a \right)}}$$
/ ___________ \
| ___ / ___ |
2/ 3*pi\ | ___ \/ 2 *\/ 5 - \/ 5 *sin(2*a)|
sin |-----|*|1 + \/ 5 - -----------------------------|
\2 + a/ | 2 |
\ 2*sin (a) /
-------------------------------------------------------
/ 6*pi\
2*sin|-----|
\2 + a/
$$\frac{\left(1 + \sqrt{5} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}}\right) \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}}{2 \sin{\left(\frac{6 \pi}{a + 2} \right)}}$$
/ 3*pi\ / pi\
sec|-----|*sec|a - --|
\2 + a/ \ 2 /
--------------------------------
/ 7*pi\ / pi 3*pi\
sec|-a + ----|*sec|- -- + -----|
\ 10 / \ 2 2 + a/
$$\frac{\sec{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \sec{\left(- a + \frac{7 \pi}{10} \right)}}$$
/ 3*pi\ / 3*pi\
-cos|a + ----|*sin|-----|
\ 10 / \2 + a/
--------------------------
/ 3*pi\
cos|-----|*sin(a)
\2 + a/
$$- \frac{\sin{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}{\sin{\left(a \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)}}$$
2/a 2*pi\ /a 2*pi\ / 3*pi\
2*sin |- + ----|*cot(a)*cot|- + ----|*tan|-----|
\2 5 / \2 5 / \2 + a/
------------------------------------------------
/ 2/a\\ 2/a\
|-1 + tan |-||*cos |-|
\ \2// \2/
$$\frac{2 \sin^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \cos^{2}{\left(\frac{a}{2} \right)}}$$
/ ___________\
| ___ / ___ |
| ___ \/ 2 *\/ 5 - \/ 5 | / 3*pi\
|1 + \/ 5 - --------------------|*tan|-----|
\ tan(a) / \2 + a/
---------------------------------------------
4
$$\frac{\left(1 + \sqrt{5} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{\tan{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4}$$
/ ___________ \
| ___ / ___ |
| ___ \/ 2 *\/ 5 - \/ 5 *cos(a)| / pi 3*pi\
|1 + \/ 5 - ---------------------------|*cos|- -- + -----|
| / pi\ | \ 2 2 + a/
| cos|a - --| |
\ \ 2 / /
-----------------------------------------------------------
/ 3*pi\
4*cos|-----|
\2 + a/
$$\frac{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + 1 + \sqrt{5}\right) \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}{4 \cos{\left(\frac{3 \pi}{a + 2} \right)}}$$
2/ 3*pi\ 2/a 2*pi\
4*sin |-----|*sin |- + ----|*sin(2*a)
\2 + a/ \2 5 /
-------------------------------------------------------------------------------
/ 4/a 2*pi\\
| 4*sin |- + ----|| / 2 \
| \2 5 /| | sin (a) | / 3*pi\ 2 2/a\ / 6*pi\
|1 + ----------------|*|1 - ---------|*cos|a + ----|*sin (a)*sin |-|*sin|-----|
| 2/ 3*pi\ | | 4/a\| \ 10 / \2/ \2 + a/
| cos |a + ----| | | 4*sin |-||
\ \ 10 / / \ \2//
$$\frac{4 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \sin^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\cos^{2}{\left(a + \frac{3 \pi}{10} \right)}} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}$$
___________
___ ___ / ___
1 + \/ 5 - \/ 2 *\/ 5 - \/ 5 *cot(a)
---------------------------------------
/ 3*pi\
4*cot|-----|
\2 + a/
$$\frac{- \sqrt{2} \sqrt{5 - \sqrt{5}} \cot{\left(a \right)} + 1 + \sqrt{5}}{4 \cot{\left(\frac{3 \pi}{a + 2} \right)}}$$
2
/ 2/a\\ / 3*pi\ /a 2*pi\
|1 + tan |-|| *tan|-----|*tan|- + ----|
\ \4// \2 + a/ \2 5 /
---------------------------------------------------
/ 2/a 2*pi\\ / 1 \ 2/a\
2*|1 + tan |- + ----||*|1 - -------|*tan(a)*tan |-|
\ \2 5 // | 2/a\| \4/
| tan |-||
\ \2//
$$\frac{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{2 \left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \tan^{2}{\left(\frac{a}{4} \right)} \tan{\left(a \right)}}$$
/ ___________ \
| ___ / ___ |
2/ 3*pi\ | ___ \/ 2 *\/ 5 - \/ 5 *sin(2*a)|
-sin |-----|*|-1 - \/ 5 + -----------------------------|
\2 + a/ | 2 |
\ 2*sin (a) /
----------------------------------------------------------
/ 6*pi\
2*sin|-----|
\2 + a/
$$- \frac{\left(- \sqrt{5} - 1 + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}}\right) \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)}}{2 \sin{\left(\frac{6 \pi}{a + 2} \right)}}$$
/ ___________ \
| ___ ___ / ___ |
-\-1 - \/ 5 + \/ 2 *\/ 5 - \/ 5 *cot(a)/
--------------------------------------------
/ 3*pi\
4*cot|-----|
\2 + a/
$$- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \cot{\left(a \right)} - \sqrt{5} - 1}{4 \cot{\left(\frac{3 \pi}{a + 2} \right)}}$$
/a pi\ / pi 3*pi\
2*cos(a)*cos|- - --|*cos|- -- + -----|
\2 10/ \ 2 2 + a/
-----------------------------------------------------------------------------------------
/ 2/a pi\ \ / 2/a\ \
| cos |- - --| | | cos |-| |
| \2 10/ | | \2/ | / 3*pi\ / pi\ 2/a pi\ /a 2*pi\
|1 + --------------|*|1 - ------------|*cos|-----|*cos|a - --|*cos |- - --|*cos|- + ----|
| 2/a 2*pi\| | 2/a pi\| \2 + a/ \ 2 / \2 2 / \2 5 /
| cos |- + ----|| | cos |- - --||
\ \2 5 // \ \2 2 //
$$\frac{2 \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{10} \right)}}{\left(- \frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \left(\frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{10} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} + 1\right) \cos{\left(\frac{3 \pi}{a + 2} \right)} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \cos{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}$$
/a pi\ /a 2*pi\ / pi 3*pi\
2*cos(a)*cos|- - --|*cos|- + ----|*cos|- -- + -----|
\2 10/ \2 5 / \ 2 2 + a/
----------------------------------------------------
/ 2/a pi\\
| cos |- - --||
| \2 2 /| 2/a\ / 3*pi\ / pi\
|-1 + ------------|*cos |-|*cos|-----|*cos|a - --|
| 2/a\ | \2/ \2 + a/ \ 2 /
| cos |-| |
\ \2/ /
$$\frac{2 \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{10} \right)} \cos{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(-1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos^{2}{\left(\frac{a}{2} \right)} \cos{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}$$
/ ___________ \
| ___ ___ / ___ | / 3*pi\
-\-1 - \/ 5 + \/ 2 *\/ 5 - \/ 5 *cot(a)/*tan|-----|
\2 + a/
-------------------------------------------------------
4
$$- \frac{\left(\sqrt{2} \sqrt{5 - \sqrt{5}} \cot{\left(a \right)} - \sqrt{5} - 1\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4}$$
2/a pi\ 4/a pi\ /a 2*pi\ / 3*pi\
8*cot |- + --|*sin |- + --|*cot(a)*cot|- + ----|*tan|-----|
\4 5 / \4 5 / \2 5 / \2 + a/
-----------------------------------------------------------
2
/ 2/a\\ / 2/a\\ 4/a\
|-1 + cot |-|| *|-1 + tan |-||*sin |-|
\ \4// \ \2// \4/
$$\frac{8 \sin^{4}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(a \right)} \cot^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{a}{4} \right)}}$$
/ 1 \ /a 2*pi\
2*|1 + -------|*cot(a)*cot|- + ----|
| 2/a\| \2 5 /
| cot |-||
\ \2//
----------------------------------------------
/ 2/a 2*pi\\ / 1 \ / 3*pi\
|1 + cot |- + ----||*|-1 + -------|*cot|-----|
\ \2 5 // | 2/a\| \2 + a/
| cot |-||
\ \2//
$$\frac{2 \left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(-1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \cot{\left(\frac{3 \pi}{a + 2} \right)}}$$
/ 3*pi\
-csc(a)*sec|-----|
\2 + a/
-----------------------
/ 3*pi\ / pi\
csc|-----|*csc|-a + --|
\2 + a/ \ 5 /
$$- \frac{\csc{\left(a \right)} \sec{\left(\frac{3 \pi}{a + 2} \right)}}{\csc{\left(\frac{3 \pi}{a + 2} \right)} \csc{\left(- a + \frac{\pi}{5} \right)}}$$
2/pi a\ /pi 3*pi\
2*csc |-- - -|*csc(a)*csc|-- - -----|
\2 2/ \2 2 + a/
----------------------------------------------------------------------
/ 2/pi a\\
| csc |-- - -||
| \2 2/| / 3*pi\ /pi \ /a 2*pi\ / a pi\
|-1 + ------------|*csc|-----|*csc|-- - a|*csc|- + ----|*csc|- - + --|
| 2/a\ | \2 + a/ \2 / \2 5 / \ 2 10/
| csc |-| |
\ \2/ /
$$\frac{2 \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)} \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(-1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(\frac{3 \pi}{a + 2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{10} \right)} \csc{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}$$
/ 1 1 \ / 3*pi\
4*|- - - --------|*cos(a)*csc(a)*sin|-----|
\ 2 2*cos(a)/ \2 + a/
---------------------------------------------------
/ 3*pi\ /a 2*pi\ / a pi\
(1 + cos(a))*cos|-----|*csc|- + ----|*csc|- - + --|
\2 + a/ \2 5 / \ 2 10/
$$\frac{4 \left(- \frac{1}{2} - \frac{1}{2 \cos{\left(a \right)}}\right) \sin{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a \right)} \csc{\left(a \right)}}{\left(\cos{\left(a \right)} + 1\right) \cos{\left(\frac{3 \pi}{a + 2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{10} \right)} \csc{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}$$
2
/ 2/a\\ 2/a pi\ / 3*pi\
8*|1 + tan |-|| *tan |- + --|*tan|-----|
\ \4// \4 5 / \2 + a/
----------------------------------------------------------------------
2 2
/ 2/a pi\\ / 2/a\\ / 2/a\\ /a 2*pi\
|1 + tan |- + --|| *|1 - tan |-|| *|-1 + tan |-||*tan(a)*tan|- + ----|
\ \4 5 // \ \4// \ \2// \2 5 /
$$\frac{8 \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)}}{\left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\tan^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} + 1\right)^{2} \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}$$
2/a\ / 3*pi\ /a 2*pi\
tan |-|*cot(a)*tan|-----|*tan|- + ----|
\4/ \2 + a/ \2 5 /
--------------------------------------------
/ 2/a 2*pi\\ / 2/a\\ 4/a\
2*|1 + tan |- + ----||*|1 - cot |-||*sin |-|
\ \2 5 // \ \2// \4/
$$\frac{\tan^{2}{\left(\frac{a}{4} \right)} \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} \cot{\left(a \right)}}{2 \left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \sin^{4}{\left(\frac{a}{4} \right)}}$$
2/ 3*pi\ 2/a 2*pi\
8*sin |-----|*sin |- + ----|*sin(2*a)
\2 + a/ \2 5 /
------------------------------------------------------------------------------------
/ 4/a 2*pi\\
| 4*sin |- + ----|| / 2 \
| \2 5 /| | sin (a) | / 3*pi\ 2 / 6*pi\
(1 - cos(a))*|1 + ----------------|*|1 - ---------|*cos|a + ----|*sin (a)*sin|-----|
| 2/ 3*pi\ | | 4/a\| \ 10 / \2 + a/
| cos |a + ----| | | 4*sin |-||
\ \ 10 / / \ \2//
$$\frac{8 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \sin^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(1 - \cos{\left(a \right)}\right) \left(\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\cos^{2}{\left(a + \frac{3 \pi}{10} \right)}} + 1\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}$$
/ 1 \ / 3*pi\ /a 2*pi\
2*|1 + -------|*tan|-----|*tan|- + ----|
| 2/a\| \2 + a/ \2 5 /
| tan |-||
\ \2//
-----------------------------------------
/ 2/a 2*pi\\ / 1 \
|1 + tan |- + ----||*|1 - -------|*tan(a)
\ \2 5 // | 2/a\|
| tan |-||
\ \2//
$$\frac{2 \left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \tan{\left(a \right)}}$$
/ 1 \ / 3*pi\ /a 2*pi\
|1 - ------|*tan|-----|*tan|- + ----|
\ cos(a)/ \2 + a/ \2 5 /
---------------------------------------------
/ 2/a 2*pi\\ 4/a\ 2/a\
4*|1 + tan |- + ----||*cos |-|*tan(a)*tan |-|
\ \2 5 // \4/ \4/
$$\frac{\left(1 - \frac{1}{\cos{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{4 \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \cos^{4}{\left(\frac{a}{4} \right)} \tan^{2}{\left(\frac{a}{4} \right)} \tan{\left(a \right)}}$$
2/ 3*pi\ / 3*pi\
sin |-----|*cos|a + ----|*sin(2*a)
\2 + a/ \ 10 /
------------------------------------------------
/ 4/a\\
| 4*sin |-||
| \2/| 2 / 6*pi\ 2/pi a\
|-1 + ---------|*sin (a)*sin|-----|*sin |-- + -|
| 2 | \2 + a/ \2 2/
\ sin (a) /
$$\frac{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} - 1\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)} \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}}$$
2
/ 2/a\\
|1 + cot |-|| *cot(a)
\ \4//
---------------------------------------------------------------------
/ 1 \ / 2/a\\ 2/a\ / 3*pi\ /a 2*pi\
2*|1 + --------------|*|1 - cot |-||*cot |-|*cot|-----|*cot|- + ----|
| 2/a 2*pi\| \ \2// \4/ \2 + a/ \2 5 /
| cot |- + ----||
\ \2 5 //
$$\frac{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \cot{\left(a \right)}}{2 \left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}\right) \cot^{2}{\left(\frac{a}{4} \right)} \cot{\left(\frac{3 \pi}{a + 2} \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}$$
2/ 3*pi\ / 3*pi\
2*sin |-----|*cos|a + ----|*sin(2*a)
\2 + a/ \ 10 /
------------------------------------------------
/ 4/a\\
| 4*sin |-||
| \2/| 2 / 6*pi\
(1 + cos(a))*|-1 + ---------|*sin (a)*sin|-----|
| 2 | \2 + a/
\ sin (a) /
$$\frac{2 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{3 \pi}{a + 2} \right)} \cos{\left(a + \frac{3 \pi}{10} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} - 1\right) \left(\cos{\left(a \right)} + 1\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{6 \pi}{a + 2} \right)}}$$
2
/ 2/a\\ 2/a pi\ /a 2*pi\
8*|1 + cot |-|| *cot |- + --|*cot(a)*cot|- + ----|
\ \4// \4 5 / \2 5 /
-------------------------------------------------------------
2 2
/ 2/a pi\\ / 1 \ / 2/a\\ / 3*pi\
|1 + cot |- + --|| *|-1 + -------|*|-1 + cot |-|| *cot|-----|
\ \4 5 // | 2/a\| \ \4// \2 + a/
| cot |-||
\ \2//
$$\frac{8 \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \cot{\left(a \right)} \cot^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(-1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} + 1\right)^{2} \cot{\left(\frac{3 \pi}{a + 2} \right)}}$$
2/a pi\ / 3*pi\
8*tan |- + --|*tan|-----|
\4 5 / \2 + a/
------------------------------------------------------------------------------
2 2
/ 2/a pi\\ / 2/a\\ / 2/a\\ 4/a\ /a 2*pi\
|1 + tan |- + --|| *|1 - tan |-|| *|-1 + tan |-||*cos |-|*tan(a)*tan|- + ----|
\ \4 5 // \ \4// \ \2// \4/ \2 5 /
$$\frac{8 \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)}}{\left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\tan^{2}{\left(\frac{a}{4} + \frac{\pi}{5} \right)} + 1\right)^{2} \cos^{4}{\left(\frac{a}{4} \right)} \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}$$
2/a pi\ / 3*pi\ / pi\ /a 2*pi\
2*sec |- - --|*sec|-----|*sec|a - --|*sec|- + ----|
\2 2 / \2 + a/ \ 2 / \2 5 /
----------------------------------------------------------------------------
/ 2/a 2*pi\\ / 2/a pi\\
| sec |- + ----|| | sec |- - --||
| \2 5 /| | \2 2 /| /a pi\ / pi 3*pi\
|1 + --------------|*|1 - ------------|*sec(a)*sec|- - --|*sec|- -- + -----|
| 2/a pi\ | | 2/a\ | \2 10/ \ 2 2 + a/
| sec |- - --| | | sec |-| |
\ \2 10/ / \ \2/ /
$$\frac{2 \sec{\left(\frac{3 \pi}{a + 2} \right)} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \sec{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{10} \right)}}\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{10} \right)}}$$
/ 3*pi\ /a 2*pi\
2*tan|-----|*tan|- + ----|
\2 + a/ \2 5 /
-------------------------------------------------
/ 2/a 2*pi\\ / 2/a\\ 2/a\
|1 + tan |- + ----||*|1 - cot |-||*sin |-|*tan(a)
\ \2 5 // \ \2// \2/
$$\frac{2 \tan{\left(\frac{3 \pi}{a + 2} \right)} \tan{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(1 - \cot^{2}{\left(\frac{a}{2} \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)}}$$
/ ___________\
| ___ / ___ |
| ___ \/ 2 *\/ 5 - \/ 5 | / 3*pi\
-|-1 - \/ 5 + --------------------|*tan|-----|
\ tan(a) / \2 + a/
------------------------------------------------
4
$$- \frac{\left(- \sqrt{5} - 1 + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{\tan{\left(a \right)}}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{4}$$
/ ___________ \
| ___ / ___ |
| ___ \/ 2 *\/ 5 - \/ 5 *csc(a)| /pi 3*pi\
|1 + \/ 5 - ---------------------------|*csc|-- - -----|
| /pi \ | \2 2 + a/
| csc|-- - a| |
\ \2 / /
---------------------------------------------------------
/ 3*pi\
4*csc|-----|
\2 + a/
$$\frac{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + 1 + \sqrt{5}\right) \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)}}{4 \csc{\left(\frac{3 \pi}{a + 2} \right)}}$$
2
/ _____________ \ / _____________ \
| / ___ /a\| | / ___ /a\| / 3*pi\
|-1 + \/ 5 + 2*\/ 5 *tan|-|| *(-1 + cos(a))*|\/ 5 + 2*\/ 5 + tan|-||*tan|-----|
\ \2// \ \2// \2 + a/
------------------------------------------------------------------------------------
/ _____________ \
| / ___ /a\| / ___\ 2/a\
2*|1 - \/ 5 + 2*\/ 5 *tan|-||*\3 + \/ 5 /*sin(a)*tan |-|
\ \2// \2/
$$\frac{\left(\sqrt{2 \sqrt{5} + 5} \tan{\left(\frac{a}{2} \right)} - 1\right)^{2} \left(\cos{\left(a \right)} - 1\right) \left(\tan{\left(\frac{a}{2} \right)} + \sqrt{2 \sqrt{5} + 5}\right) \tan{\left(\frac{3 \pi}{a + 2} \right)}}{2 \left(\sqrt{5} + 3\right) \left(- \sqrt{2 \sqrt{5} + 5} \tan{\left(\frac{a}{2} \right)} + 1\right) \sin{\left(a \right)} \tan^{2}{\left(\frac{a}{2} \right)}}$$
/ 2/a\\ /a 2*pi\
2*|1 + tan |-||*cot(a)*cot|- + ----|
\ \2// \2 5 /
----------------------------------------------
/ 2/a 2*pi\\ / 2/a\\ / 3*pi\
|1 + cot |- + ----||*|-1 + tan |-||*cot|-----|
\ \2 5 // \ \2// \2 + a/
$$\frac{2 \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \cot{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)} + 1\right) \cot{\left(\frac{3 \pi}{a + 2} \right)}}$$
/ ___________ \
| ___ / ___ / pi\|
| \/ 2 *\/ 5 - \/ 5 *sec|a - --||
| ___ \ 2 /| / 3*pi\
|1 + \/ 5 - --------------------------------|*sec|-----|
\ sec(a) / \2 + a/
---------------------------------------------------------
/ pi 3*pi\
4*sec|- -- + -----|
\ 2 2 + a/
$$\frac{\left(1 + \sqrt{5} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}\right) \sec{\left(\frac{3 \pi}{a + 2} \right)}}{4 \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}$$
/pi 3*pi\
-csc(a)*csc|-- - -----|
\2 2 + a/
------------------------
/ 3*pi\ / 3*pi\
csc|-----|*sec|a + ----|
\2 + a/ \ 10 /
$$- \frac{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)}}{\csc{\left(\frac{3 \pi}{a + 2} \right)} \sec{\left(a + \frac{3 \pi}{10} \right)}}$$
/ ___________ \
| ___ / ___ |
| ___ \/ 2 *\/ 5 - \/ 5 *csc(a)| /pi 3*pi\
-|-1 - \/ 5 + ---------------------------|*csc|-- - -----|
| /pi \ | \2 2 + a/
| csc|-- - a| |
\ \2 / /
------------------------------------------------------------
/ 3*pi\
4*csc|-----|
\2 + a/
$$- \frac{\left(\frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \sqrt{5} - 1\right) \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)}}{4 \csc{\left(\frac{3 \pi}{a + 2} \right)}}$$
/ ___________ \
| ___ / ___ / pi\|
| \/ 2 *\/ 5 - \/ 5 *sec|a - --||
| ___ \ 2 /| / 3*pi\
-|-1 - \/ 5 + --------------------------------|*sec|-----|
\ sec(a) / \2 + a/
------------------------------------------------------------
/ pi 3*pi\
4*sec|- -- + -----|
\ 2 2 + a/
$$- \frac{\left(- \sqrt{5} - 1 + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}\right) \sec{\left(\frac{3 \pi}{a + 2} \right)}}{4 \sec{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}$$
2/a\ /pi 3*pi\ / a pi\
2*csc |-|*csc(a)*csc|-- - -----|*csc|- - + --|
\2/ \2 2 + a/ \ 2 10/
----------------------------------------------------------------------------
/ 2/ a pi\\ / 2/a\ \
| csc |- - + --|| | csc |-| |
| \ 2 10/| | \2/ | / 3*pi\ /pi \ /a 2*pi\
|1 + --------------|*|1 - ------------|*csc|-----|*csc|-- - a|*csc|- + ----|
| 2/a 2*pi\| | 2/pi a\| \2 + a/ \2 / \2 5 /
| csc |- + ----|| | csc |-- - -||
\ \2 5 // \ \2 2//
$$\frac{2 \csc^{2}{\left(\frac{a}{2} \right)} \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{3 \pi}{a + 2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{10} \right)}}{\left(- \frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right) \left(\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{10} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}} + 1\right) \csc{\left(\frac{3 \pi}{a + 2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(\frac{a}{2} + \frac{2 \pi}{5} \right)}}$$
/ ___________ \
| ___ / ___ |
| ___ \/ 2 *\/ 5 - \/ 5 *cos(a)| / pi 3*pi\
-|-1 - \/ 5 + ---------------------------|*cos|- -- + -----|
| / pi\ | \ 2 2 + a/
| cos|a - --| |
\ \ 2 / /
--------------------------------------------------------------
/ 3*pi\
4*cos|-----|
\2 + a/
$$- \frac{\left(\frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} - \sqrt{5} - 1\right) \cos{\left(- \frac{\pi}{2} + \frac{3 \pi}{a + 2} \right)}}{4 \cos{\left(\frac{3 \pi}{a + 2} \right)}}$$
-(-1 - sqrt(5) + sqrt(2)*sqrt(5 - sqrt(5))*cos(a)/cos(a - pi/2))*cos(-pi/2 + 3*pi/(2 + a))/(4*cos(3*pi/(2 + a)))