Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a)
¿Cómo vas a descomponer esta tan(16*pi/5)*tan(pi+a)-cos(pi/(2+a))*sin(pi+a) expresión en fracciones?
Solución
Ha introducido
[src]
/16*pi\ / pi \ tan|-----|*tan(pi + a) - cos|-----|*sin(pi + a) \ 5 / \2 + a/
$$- \sin{\left(a + \pi \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \tan{\left(\frac{16 \pi}{5} \right)} \tan{\left(a + \pi \right)}$$
tan((16*pi)/5)*tan(pi + a) - cos(pi/(2 + a))*sin(pi + a)
Simplificación general
[src]
_____________
/ ___ / pi \
\/ 5 - 2*\/ 5 *tan(a) + cos|-----|*sin(a)
\2 + a/
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)}$$
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Denominador racional
[src]
_____________
/ ___ / pi \
\/ 5 - 2*\/ 5 *tan(a) + cos|-----|*sin(a)
\2 + a/
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)}$$
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Respuesta numérica
[src]
0.726542528005361*tan(pi + a) - cos(pi/(2 + a))*sin(pi + a)
0.726542528005361*tan(pi + a) - cos(pi/(2 + a))*sin(pi + a)
Denominador común
[src]
_____________
/ ___ / pi \
\/ 5 - 2*\/ 5 *tan(pi + a) - cos|-----|*sin(pi + a)
\2 + a/
$$- \sin{\left(a + \pi \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a + \pi \right)}$$
sqrt(5 - 2*sqrt(5))*tan(pi + a) - cos(pi/(2 + a))*sin(pi + a)
Unión de expresiones racionales
[src]
_____________
/ ___ / pi \
\/ 5 - 2*\/ 5 *tan(a) + cos|-----|*sin(a)
\2 + a/
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)}$$
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Combinatoria
[src]
_____________
/ ___ / pi \
\/ 5 - 2*\/ 5 *tan(a) + cos|-----|*sin(a)
\2 + a/
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)}$$
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Potencias
[src]
/ pi*I -pi*I \
| ----- ------|
| 2 + a 2 + a | / -4*pi*I 4*pi*I\
|e e | / I*(-pi - a) I*(pi + a)\ | ------- ------|
I*|------ + -------|*\- e + e / / I*(pi + a) I*(-pi - a)\ | 5 5 |
\ 2 2 / \- e + e /*\- e + e /
--------------------------------------------------- - -----------------------------------------------------
2 / -4*pi*I 4*pi*I\
| ------- ------|
/ I*(pi + a) I*(-pi - a)\ | 5 5 |
\e + e /*\e + e /
$$\frac{i \left(- e^{i \left(- a - \pi\right)} + e^{i \left(a + \pi\right)}\right) \left(\frac{e^{\frac{i \pi}{a + 2}}}{2} + \frac{e^{- \frac{i \pi}{a + 2}}}{2}\right)}{2} - \frac{\left(e^{\frac{4 i \pi}{5}} - e^{- \frac{4 i \pi}{5}}\right) \left(e^{i \left(- a - \pi\right)} - e^{i \left(a + \pi\right)}\right)}{\left(e^{- \frac{4 i \pi}{5}} + e^{\frac{4 i \pi}{5}}\right) \left(e^{i \left(- a - \pi\right)} + e^{i \left(a + \pi\right)}\right)}$$
_____________
/ ___ / pi \
\/ 5 - 2*\/ 5 *tan(a) + cos|-----|*sin(a)
\2 + a/
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)}$$
sqrt(5 - 2*sqrt(5))*tan(a) + cos(pi/(2 + a))*sin(a)
Parte trigonométrica
[src]
/ 2/ pi \\ /a\
_____________ 2*|1 - tan |---------||*cot|-|
/ ___ \ \2*(2 + a)// \2/
\/ 5 - 2*\/ 5 *tan(a) + -----------------------------------
/ 2/a\\ / 2/ pi \\
|1 + cot |-||*|1 + tan |---------||
\ \2// \ \2*(2 + a)//
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \cot{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)}$$
___ 2
/pi pi \ 2*\/ 5 *sin (a)
sin(a)*sin|-- + -----| + -------------------------
\2 2 + a/ _____________
/ ___
\/ 5 + 2*\/ 5 *sin(2*a)
$$\frac{2 \sqrt{5} \sin^{2}{\left(a \right)}}{\sqrt{2 \sqrt{5} + 5} \sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)}$$
/ ___\
|5 \/ 5 | /pi \
|- - -----|*csc|-- - a|
1 \4 4 / \2 /
---------------------- + -----------------------
/pi pi \ ___________
csc(a)*csc|-- - -----| / ___
\2 2 + a/ / 5 \/ 5
/ - + ----- *csc(a)
\/ 8 8
$$\frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \csc{\left(- a + \frac{\pi}{2} \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}}$$
/ 2/ pi \\ /a\
2*|-1 + cot |---------||*tan|-|
1 \ \2*(2 + a)// \2/
------------------------- + -----------------------------------
_____________ / 2/ pi \\ / 2/a\\
/ ___ |1 + cot |---------||*|1 + tan |-||
/ 2*\/ 5 \ \2*(2 + a)// \ \2//
/ 1 + ------- *cot(a)
\/ 5
$$\frac{1}{\sqrt{\frac{2 \sqrt{5}}{5} + 1} \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)}$$
___________
/ ___
/ 5 \/ 5 / 2/ pi \\ /a\
/ - - ----- *tan(a) 2*|1 - tan |---------||*tan|-|
\/ 8 8 \ \2*(2 + a)// \2/
- ----------------------- + -----------------------------------
___ / 2/a\\ / 2/ pi \\
1 \/ 5 |1 + tan |-||*|1 + tan |---------||
- - - ----- \ \2// \ \2*(2 + a)//
4 4
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \tan{\left(a \right)}}{- \frac{\sqrt{5}}{4} - \frac{1}{4}}$$
_____________
/ ___ /pi \
\/ 5 - 2*\/ 5 *csc|-- - a|
1 \2 /
---------------------- + ----------------------------
/pi pi \ csc(a)
csc(a)*csc|-- - -----|
\2 2 + a/
$$\frac{\sqrt{5 - 2 \sqrt{5}} \csc{\left(- a + \frac{\pi}{2} \right)}}{\csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}}$$
___________
/ ___
/ 5 \/ 5
/ - - ----- *sec(a)
1 \/ 8 8
----------------- - -----------------------
/ pi \ / ___\
csc(a)*sec|-----| | 1 \/ 5 |
\2 + a/ |- - - -----|*csc(a)
\ 4 4 /
$$- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sec{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \sec{\left(\frac{\pi}{a + 2} \right)}}$$
___________
___ / ___ /pi \
\/ 2 *\/ 5 - \/ 5 *csc|-- - a|
1 \2 /
---------------------- - --------------------------------
/pi pi \ / ___\
csc(a)*csc|-- - -----| | 1 \/ 5 |
\2 2 + a/ 4*|- - - -----|*csc(a)
\ 4 4 /
$$- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \csc{\left(- a + \frac{\pi}{2} \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}}$$
___ / pi\
\/ 5 *cos|a - --|
/ pi \ / pi\ \ 2 /
cos|-----|*cos|a - --| + -----------------------
\2 + a/ \ 2 / _____________
/ ___
\/ 5 + 2*\/ 5 *cos(a)
$$\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} + \frac{\sqrt{5} \cos{\left(a - \frac{\pi}{2} \right)}}{\sqrt{2 \sqrt{5} + 5} \cos{\left(a \right)}}$$
/ 2/ pi \\ /a\ ___________
2*|-1 + cot |---------||*cot|-| ___ / ___
\ \2*(2 + a)// \2/ \/ 2 *\/ 5 - \/ 5
----------------------------------- - ----------------------
/ 2/a\\ / 2/ pi \\ / ___\
|1 + cot |-||*|1 + cot |---------|| | 1 \/ 5 |
\ \2// \ \2*(2 + a)// 4*|- - - -----|*cot(a)
\ 4 4 /
$$- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)}$$
___________
/ ___
/ 5 \/ 5 2
2* / - - ----- *sin (a)
/pi pi \ \/ 8 8
sin(a)*sin|-- + -----| - --------------------------
\2 2 + a/ / ___\
| 1 \/ 5 |
|- - - -----|*sin(2*a)
\ 4 4 /
$$- \frac{2 \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin^{2}{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)}$$
/ 2/ pi \\ /a\ ___________
2*|1 - tan |---------||*tan|-| ___ / ___
\ \2*(2 + a)// \2/ \/ 2 *\/ 5 - \/ 5 *tan(a)
----------------------------------- - ---------------------------
/ 2/a\\ / 2/ pi \\ / ___\
|1 + tan |-||*|1 + tan |---------|| | 1 \/ 5 |
\ \2// \ \2*(2 + a)// 4*|- - - -----|
\ 4 4 /
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \tan{\left(a \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)}$$
_____________
/ ___ / pi \
\/ 5 - 2*\/ 5 *tan(a) + cos|-----|*sin(a)
\2 + a/
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)}$$
___
1 \/ 5 *sec(a)
---------------------- + ----------------------------
/ pi \ / pi\ _____________
sec|-----|*sec|a - --| / ___ / pi\
\2 + a/ \ 2 / \/ 5 + 2*\/ 5 *sec|a - --|
\ 2 /
$$\frac{\sqrt{5} \sec{\left(a \right)}}{\sqrt{2 \sqrt{5} + 5} \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
___
5 \/ 5 / 2/ pi \\ /a\
- - ----- 2*|-1 + cot |---------||*cot|-|
4 4 \ \2*(2 + a)// \2/
----------------------- + -----------------------------------
___________ / 2/a\\ / 2/ pi \\
/ ___ |1 + cot |-||*|1 + cot |---------||
/ 5 \/ 5 \ \2// \ \2*(2 + a)//
/ - + ----- *cot(a)
\/ 8 8
$$\frac{\frac{5}{4} - \frac{\sqrt{5}}{4}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)}$$
___________
___ / ___ 2
/pi pi \ \/ 2 *\/ 5 - \/ 5 *sin (a)
sin(a)*sin|-- + -----| - ----------------------------
\2 2 + a/ / ___\
| 1 \/ 5 |
2*|- - - -----|*sin(2*a)
\ 4 4 /
$$- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sin^{2}{\left(a \right)}}{2 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)}$$
/ ___\
2 |5 \/ 5 |
2*sin (a)*|- - -----|
/pi pi \ \4 4 /
sin(a)*sin|-- + -----| + -------------------------
\2 2 + a/ ___________
/ ___
/ 5 \/ 5
/ - + ----- *sin(2*a)
\/ 8 8
$$\frac{2 \left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \sin^{2}{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)}$$
/ ___\
|5 \/ 5 | / 2/ pi \\ /a\
|- - -----|*tan(a) 2*|1 - tan |---------||*tan|-|
\4 4 / \ \2*(2 + a)// \2/
------------------ + -----------------------------------
___________ / 2/a\\ / 2/ pi \\
/ ___ |1 + tan |-||*|1 + tan |---------||
/ 5 \/ 5 \ \2// \ \2*(2 + a)//
/ - + -----
\/ 8 8
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)} + \frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \tan{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}$$
___________
/ ___
/ 5 \/ 5
/ - - ----- *tan(a)
/ pi \ \/ 8 8
cos|-----|*sin(a) - -----------------------
\2 + a/ ___
1 \/ 5
- - - -----
4 4
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \tan{\left(a \right)}}{- \frac{\sqrt{5}}{4} - \frac{1}{4}}$$
___________
/ ___
/ 5 \/ 5
/ - - ----- *sec(a)
1 \/ 8 8
- ---------------------- - -------------------------
/ pi \ / pi\ / ___\
sec|-----|*sec|a + --| | 1 \/ 5 | / pi\
\2 + a/ \ 2 / |- - - -----|*sec|a - --|
\ 4 4 / \ 2 /
$$- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sec{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sec{\left(a - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a + \frac{\pi}{2} \right)}}$$
___
/ pi \ \/ 5 *tan(a)
cos|-----|*sin(a) + ----------------
\2 + a/ _____________
/ ___
\/ 5 + 2*\/ 5
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \frac{\sqrt{5} \tan{\left(a \right)}}{\sqrt{2 \sqrt{5} + 5}}$$
/ 2/ pi \\ /a\
___ 2*|-1 + cot |---------||*cot|-|
\/ 5 \ \2*(2 + a)// \2/
----------------------- + -----------------------------------
_____________ / 2/a\\ / 2/ pi \\
/ ___ |1 + cot |-||*|1 + cot |---------||
\/ 5 + 2*\/ 5 *cot(a) \ \2// \ \2*(2 + a)//
$$\frac{\sqrt{5}}{\sqrt{2 \sqrt{5} + 5} \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)}$$
___ /pi \
\/ 5 *csc|-- - a|
1 \2 /
---------------------- + -----------------------
/pi pi \ _____________
csc(a)*csc|-- - -----| / ___
\2 2 + a/ \/ 5 + 2*\/ 5 *csc(a)
$$\frac{\sqrt{5} \csc{\left(- a + \frac{\pi}{2} \right)}}{\sqrt{2 \sqrt{5} + 5} \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}}$$
___________
/ ___
/ 5 \/ 5 / pi\
/ - - ----- *cos|a - --|
/ pi \ / pi\ \/ 8 8 \ 2 /
cos|-----|*cos|a - --| - ----------------------------
\2 + a/ \ 2 / / ___\
| 1 \/ 5 |
|- - - -----|*cos(a)
\ 4 4 /
$$\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \cos{\left(a - \frac{\pi}{2} \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cos{\left(a \right)}}$$
/ pi \ / pi \ ___________
sin|a + -----| + sin|a - -----| ___ / ___
\ 2 + a/ \ 2 + a/ \/ 2 *\/ 5 - \/ 5 *tan(a)
------------------------------- - ---------------------------
2 / ___\
| 1 \/ 5 |
4*|- - - -----|
\ 4 4 /
$$\frac{\sin{\left(a - \frac{\pi}{a + 2} \right)} + \sin{\left(a + \frac{\pi}{a + 2} \right)}}{2} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \tan{\left(a \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)}$$
/ ___\
|5 \/ 5 |
|- - -----|*sec(a)
1 \4 4 /
---------------------- + ----------------------------
/ pi \ / pi\ ___________
sec|-----|*sec|a - --| / ___
\2 + a/ \ 2 / / 5 \/ 5 / pi\
/ - + ----- *sec|a - --|
\/ 8 8 \ 2 /
$$\frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \sec{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
___________
/ ___
/ 5 \/ 5
/ - - ----- *sin(a)
/ pi \ \/ 8 8
cos|-----|*sin(a) - -----------------------
\2 + a/ / ___\
| 1 \/ 5 |
|- - - -----|*cos(a)
\ 4 4 /
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sin{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cos{\left(a \right)}}$$
/ 2/ pi \\
_____________ 2*|1 - tan |---------||
/ ___ \ \2*(2 + a)//
\/ 5 - 2*\/ 5 *tan(a) + ------------------------------------------
/ 1 \ / 2/ pi \\ /a\
|1 + -------|*|1 + tan |---------||*tan|-|
| 2/a\| \ \2*(2 + a)// \2/
| tan |-||
\ \2//
$$\sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)} + \frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right)}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)}}$$
_____________ / 2/ pi \\ /a\
/ ___ 2*|-1 + cot |---------||*cot|-|
\/ 5 - 2*\/ 5 \ \2*(2 + a)// \2/
---------------- + -----------------------------------
cot(a) / 2/a\\ / 2/ pi \\
|1 + cot |-||*|1 + cot |---------||
\ \2// \ \2*(2 + a)//
$$\frac{\sqrt{5 - 2 \sqrt{5}}}{\cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)}$$
/ ___\
/ pi \ / pi \ |5 \/ 5 |
sin|a + -----| + sin|a - -----| |- - -----|*tan(a)
\ 2 + a/ \ 2 + a/ \4 4 /
------------------------------- + ------------------
2 ___________
/ ___
/ 5 \/ 5
/ - + -----
\/ 8 8
$$\frac{\sin{\left(a - \frac{\pi}{a + 2} \right)} + \sin{\left(a + \frac{\pi}{a + 2} \right)}}{2} + \frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \tan{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}$$
/ 2/ pi \\ /a\
___ 2*|1 - tan |---------||*tan|-|
\/ 5 *tan(a) \ \2*(2 + a)// \2/
---------------- + -----------------------------------
_____________ / 2/a\\ / 2/ pi \\
/ ___ |1 + tan |-||*|1 + tan |---------||
\/ 5 + 2*\/ 5 \ \2// \ \2*(2 + a)//
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)} + \frac{\sqrt{5} \tan{\left(a \right)}}{\sqrt{2 \sqrt{5} + 5}}$$
___________
___ / ___
1 \/ 2 *\/ 5 - \/ 5 *sec(a)
---------------------- - ---------------------------
/ pi \ / pi\ / ___\
sec|-----|*sec|a - --| | 1 \/ 5 | / pi\
\2 + a/ \ 2 / 4*|- - - -----|*sec|a - --|
\ 4 4 / \ 2 /
$$- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \sec{\left(a \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
/ ___\
2 |5 \/ 5 |
2*sin (a)*|- - -----|
/ pi \ \4 4 /
cos|-----|*sin(a) + -------------------------
\2 + a/ ___________
/ ___
/ 5 \/ 5
/ - + ----- *sin(2*a)
\/ 8 8
$$\frac{2 \left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \sin^{2}{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \sin{\left(2 a \right)}} + \sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)}$$
___________
/ ___
/ 5 \/ 5 / 2/ pi \\ /a\
/ - - ----- 2*|-1 + cot |---------||*cot|-|
\/ 8 8 \ \2*(2 + a)// \2/
- -------------------- + -----------------------------------
/ ___\ / 2/a\\ / 2/ pi \\
| 1 \/ 5 | |1 + cot |-||*|1 + cot |---------||
|- - - -----|*cot(a) \ \2// \ \2*(2 + a)//
\ 4 4 /
$$- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right) \cot{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)}$$
___________
___ / ___
/ pi \ \/ 2 *\/ 5 - \/ 5 *tan(a)
cos|-----|*sin(a) - ---------------------------
\2 + a/ / ___\
| 1 \/ 5 |
4*|- - - -----|
\ 4 4 /
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \tan{\left(a \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right)}$$
_____________
/ ___ 2
/pi pi \ 2*\/ 5 - 2*\/ 5 *sin (a)
sin(a)*sin|-- + -----| + --------------------------
\2 2 + a/ sin(2*a)
$$\frac{2 \sqrt{5 - 2 \sqrt{5}} \sin^{2}{\left(a \right)}}{\sin{\left(2 a \right)}} + \sin{\left(a \right)} \sin{\left(\frac{\pi}{2} + \frac{\pi}{a + 2} \right)}$$
___________
/ ___
/ 5 \/ 5 /pi \
/ - - ----- *csc|-- - a|
1 \/ 8 8 \2 /
---------------------- - ----------------------------
/pi pi \ / ___\
csc(a)*csc|-- - -----| | 1 \/ 5 |
\2 2 + a/ |- - - -----|*csc(a)
\ 4 4 /
$$- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \csc{\left(- a + \frac{\pi}{2} \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \csc{\left(a \right)}} + \frac{1}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a + 2} \right)}}$$
___________
/ ___
/ pi \ / pi \ / 5 \/ 5
sin|a + -----| + sin|a - -----| / - - ----- *tan(a)
\ 2 + a/ \ 2 + a/ \/ 8 8
------------------------------- - -----------------------
2 ___
1 \/ 5
- - - -----
4 4
$$\frac{\sin{\left(a - \frac{\pi}{a + 2} \right)} + \sin{\left(a + \frac{\pi}{a + 2} \right)}}{2} - \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \tan{\left(a \right)}}{- \frac{\sqrt{5}}{4} - \frac{1}{4}}$$
___________
___ / ___ / pi\
\/ 2 *\/ 5 - \/ 5 *cos|a - --|
/ pi \ / pi\ \ 2 /
cos|-----|*cos|a - --| - --------------------------------
\2 + a/ \ 2 / / ___\
| 1 \/ 5 |
4*|- - - -----|*cos(a)
\ 4 4 /
$$\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}} \cos{\left(a - \frac{\pi}{2} \right)}}{4 \left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cos{\left(a \right)}}$$
/27*pi\ / pi\
cos|-----|*cos|a + --|
/ pi \ / pi\ \ 10 / \ 2 /
- cos|-----|*cos|a + --| - ----------------------
\2 + a/ \ 2 / / ___\
| 1 \/ 5 |
|- - - -----|*cos(a)
\ 4 4 /
$$- \cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a + \frac{\pi}{2} \right)} - \frac{\cos{\left(\frac{27 \pi}{10} \right)} \cos{\left(a + \frac{\pi}{2} \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \cos{\left(a \right)}}$$
/ 2/ pi \\ /a\
_____________ 2*|1 - tan |---------||*tan|-|
/ ___ \ \2*(2 + a)// \2/
\/ 5 - 2*\/ 5 *tan(a) + -----------------------------------
/ 2/a\\ / 2/ pi \\
|1 + tan |-||*|1 + tan |---------||
\ \2// \ \2*(2 + a)//
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)}\right) \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\tan^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right)} + \sqrt{5 - 2 \sqrt{5}} \tan{\left(a \right)}$$
/ 2/ pi \\
2*|-1 + cot |---------||
1 \ \2*(2 + a)//
------------------------- + ------------------------------------------
_____________ / 1 \ / 2/ pi \\ /a\
/ ___ |1 + -------|*|1 + cot |---------||*cot|-|
/ 2*\/ 5 | 2/a\| \ \2*(2 + a)// \2/
/ 1 + ------- *cot(a) | cot |-||
\/ 5 \ \2//
$$\frac{1}{\sqrt{\frac{2 \sqrt{5}}{5} + 1} \cot{\left(a \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} - 1\right)}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{\pi}{2 \left(a + 2\right)} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)}}$$
_____________
/ ___
1 \/ 5 - 2*\/ 5 *sec(a)
---------------------- + -----------------------
/ pi \ / pi\ / pi\
sec|-----|*sec|a - --| sec|a - --|
\2 + a/ \ 2 / \ 2 /
$$\frac{\sqrt{5 - 2 \sqrt{5}} \sec{\left(a \right)}}{\sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
_____________
/ ___ / pi\
\/ 5 - 2*\/ 5 *cos|a - --|
/ pi \ / pi\ \ 2 /
cos|-----|*cos|a - --| + ----------------------------
\2 + a/ \ 2 / cos(a)
$$\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} + \frac{\sqrt{5 - 2 \sqrt{5}} \cos{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(a \right)}}$$
/ ___\
|5 \/ 5 | / pi\
|- - -----|*cos|a - --|
/ pi \ / pi\ \4 4 / \ 2 /
cos|-----|*cos|a - --| + -----------------------
\2 + a/ \ 2 / ___________
/ ___
/ 5 \/ 5
/ - + ----- *cos(a)
\/ 8 8
$$\cos{\left(\frac{\pi}{a + 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)} + \frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \cos{\left(a - \frac{\pi}{2} \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}} \cos{\left(a \right)}}$$
/ ___\
|5 \/ 5 |
|- - -----|*tan(a)
/ pi \ \4 4 /
cos|-----|*sin(a) + ------------------
\2 + a/ ___________
/ ___
/ 5 \/ 5
/ - + -----
\/ 8 8
$$\sin{\left(a \right)} \cos{\left(\frac{\pi}{a + 2} \right)} + \frac{\left(\frac{5}{4} - \frac{\sqrt{5}}{4}\right) \tan{\left(a \right)}}{\sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}}$$
___________
/ ___
/ 5 \/ 5
/ - - ----- *sec(a)
1 \/ 8 8
---------------------- - -------------------------
/ pi \ / pi\ / ___\
sec|-----|*sec|a - --| | 1 \/ 5 | / pi\
\2 + a/ \ 2 / |- - - -----|*sec|a - --|
\ 4 4 / \ 2 /
$$- \frac{\sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}} \sec{\left(a \right)}}{\left(- \frac{\sqrt{5}}{4} - \frac{1}{4}\right) \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(\frac{\pi}{a + 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
1/(sec(pi/(2 + a))*sec(a - pi/2)) - sqrt(5/8 - sqrt(5)/8)*sec(a)/((-1/4 - sqrt(5)/4)*sec(a - pi/2))