Parte trigonométrica
[src]
___ / pi\
\/ 2 *csc|-5*a + --|
\ 4 /
--------------------
/pi \
2*csc|-- - 10*a|
\2 /
$$\frac{\sqrt{2} \csc{\left(- 5 a + \frac{\pi}{4} \right)}}{2 \csc{\left(- 10 a + \frac{\pi}{2} \right)}}$$
___ 2 / 2/pi 5*a\\ / 2 \
\/ 2 *cos (5*a)*|1 + tan |-- + ---||*\1 - tan (5*a)/
\ \8 2 //
----------------------------------------------------
/ 2/pi 5*a\\
2*|1 - tan |-- + ---||
\ \8 2 //
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(5 a \right)}\right) \left(\tan^{2}{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(5 a \right)}}{2 \left(1 - \tan^{2}{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)}\right)}$$
cos(10*a)
--------------------------
/ pi\
- cos|5*a - --| + cos(5*a)
\ 2 /
$$\frac{\cos{\left(10 a \right)}}{\cos{\left(5 a \right)} - \cos{\left(5 a - \frac{\pi}{2} \right)}}$$
1
------------------------------------
/ 1 1 \
|-------- - -------------|*sec(10*a)
|sec(5*a) / pi\|
| sec|5*a - --||
\ \ 2 //
$$\frac{1}{\left(- \frac{1}{\sec{\left(5 a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(5 a \right)}}\right) \sec{\left(10 a \right)}}$$
1
-------------------------------
/ 1 1 \
|-------- - --------|*sec(10*a)
\sec(5*a) csc(5*a)/
$$\frac{1}{\left(\frac{1}{\sec{\left(5 a \right)}} - \frac{1}{\csc{\left(5 a \right)}}\right) \sec{\left(10 a \right)}}$$
2
1 - tan (5*a)
-----------------------------------------------
/ 2/5*a\ /5*a\ \
|1 - tan |---| 2*tan|---| |
/ 2 \ | \ 2 / \ 2 / |
\1 + tan (5*a)/*|------------- - -------------|
| 2/5*a\ 2/5*a\|
|1 + tan |---| 1 + tan |---||
\ \ 2 / \ 2 //
$$\frac{1 - \tan^{2}{\left(5 a \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{5 a}{2} \right)}}{\tan^{2}{\left(\frac{5 a}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{5 a}{2} \right)}}{\tan^{2}{\left(\frac{5 a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(5 a \right)} + 1\right)}$$
___ /pi 5*a\
2*\/ 2 *cot|-- + ---|
\8 2 /
---------------------
2/pi 5*a\
1 + cot |-- + ---|
\8 2 /
$$\frac{2 \sqrt{2} \cot{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)}}{\cot^{2}{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)} + 1}$$
___ / pi\
\/ 2 *cos|5*a - --|
\ 4 /
$$\sqrt{2} \cos{\left(5 a - \frac{\pi}{4} \right)}$$
___ /pi \
\/ 2 *sin|-- + 10*a|
\2 /
--------------------
/ 3*pi\
2*sin|5*a + ----|
\ 4 /
$$\frac{\sqrt{2} \sin{\left(10 a + \frac{\pi}{2} \right)}}{2 \sin{\left(5 a + \frac{3 \pi}{4} \right)}}$$
___ / pi\
\/ 2 *cos(10*a)*csc|-5*a + --|
\ 4 /
------------------------------
2
$$\frac{\sqrt{2} \cos{\left(10 a \right)} \csc{\left(- 5 a + \frac{\pi}{4} \right)}}{2}$$
1
-----------------------------------------
/ 1 1 \ /pi \
|------------- - --------|*csc|-- - 10*a|
| /pi \ csc(5*a)| \2 /
|csc|-- - 5*a| |
\ \2 / /
$$\frac{1}{\left(\frac{1}{\csc{\left(- 5 a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(5 a \right)}}\right) \csc{\left(- 10 a + \frac{\pi}{2} \right)}}$$
___
\/ 2
-------------
/ pi\
sec|5*a - --|
\ 4 /
$$\frac{\sqrt{2}}{\sec{\left(5 a - \frac{\pi}{4} \right)}}$$
___ / 2/pi 5*a\\ / 2 \
\/ 2 *|1 + cot |-- + ---||*\-1 + cot (5*a)/
\ \8 2 //
-------------------------------------------
/ 2 \ / 2/pi 5*a\\
2*\1 + cot (5*a)/*|-1 + cot |-- + ---||
\ \8 2 //
$$\frac{\sqrt{2} \left(\cot^{2}{\left(5 a \right)} - 1\right) \left(\cot^{2}{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)} + 1\right)}{2 \left(\cot^{2}{\left(5 a \right)} + 1\right) \left(\cot^{2}{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)} - 1\right)}$$
___ / 2/pi 5*a\\ / 2 \
\/ 2 *|1 + tan |-- + ---||*\1 - tan (5*a)/
\ \8 2 //
------------------------------------------
/ 2 \ / 2/pi 5*a\\
2*\1 + tan (5*a)/*|1 - tan |-- + ---||
\ \8 2 //
$$\frac{\sqrt{2} \left(1 - \tan^{2}{\left(5 a \right)}\right) \left(\tan^{2}{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)}\right) \left(\tan^{2}{\left(5 a \right)} + 1\right)}$$
___
\/ 2
-------------
/ pi\
csc|5*a + --|
\ 4 /
$$\frac{\sqrt{2}}{\csc{\left(5 a + \frac{\pi}{4} \right)}}$$
___ / pi\
\/ 2 *sin|5*a + --|
\ 4 /
$$\sqrt{2} \sin{\left(5 a + \frac{\pi}{4} \right)}$$
/pi \
sin|-- + 10*a|
\2 /
-------------------------
/pi \
-sin(5*a) + sin|-- + 5*a|
\2 /
$$\frac{\sin{\left(10 a + \frac{\pi}{2} \right)}}{- \sin{\left(5 a \right)} + \sin{\left(5 a + \frac{\pi}{2} \right)}}$$
___
\/ 2 *cos(10*a)
---------------
/ pi\
2*cos|5*a + --|
\ 4 /
$$\frac{\sqrt{2} \cos{\left(10 a \right)}}{2 \cos{\left(5 a + \frac{\pi}{4} \right)}}$$
___ / pi\
\/ 2 *sec|5*a + --|
\ 4 /
-------------------
2*sec(10*a)
$$\frac{\sqrt{2} \sec{\left(5 a + \frac{\pi}{4} \right)}}{2 \sec{\left(10 a \right)}}$$
___ /pi 5*a\
2*\/ 2 *tan|-- + ---|
\8 2 /
---------------------
2/pi 5*a\
1 + tan |-- + ---|
\8 2 /
$$\frac{2 \sqrt{2} \tan{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)}}{\tan^{2}{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)} + 1}$$
2
-1 + cot (5*a)
------------------------------------------------
/ 2/5*a\ /5*a\ \
|-1 + cot |---| 2*cot|---| |
/ 2 \ | \ 2 / \ 2 / |
\1 + cot (5*a)/*|-------------- - -------------|
| 2/5*a\ 2/5*a\|
|1 + cot |---| 1 + cot |---||
\ \ 2 / \ 2 //
$$\frac{\cot^{2}{\left(5 a \right)} - 1}{\left(\frac{\cot^{2}{\left(\frac{5 a}{2} \right)} - 1}{\cot^{2}{\left(\frac{5 a}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{5 a}{2} \right)}}{\cot^{2}{\left(\frac{5 a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(5 a \right)} + 1\right)}$$
___
-\/ 2 *cos(10*a)
---------------------------------------------------------
___________ ___________
___ / ___ / ___
- \/ 2 *cos(5*a) + \/ 2 + \/ 2 *\/ 2 - \/ 2 *sin(5*a)
$$- \frac{\sqrt{2} \cos{\left(10 a \right)}}{\sqrt{2 - \sqrt{2}} \sqrt{\sqrt{2} + 2} \sin{\left(5 a \right)} - \sqrt{2} \cos{\left(5 a \right)}}$$
___ / pi\
\/ 2 *cos(10*a)*sec|5*a + --|
\ 4 /
-----------------------------
2
$$\frac{\sqrt{2} \cos{\left(10 a \right)} \sec{\left(5 a + \frac{\pi}{4} \right)}}{2}$$
___ 2/pi + 20*a\ /pi 5*a\
2*\/ 2 *sin |---------|*cot|-- + ---|
\ 8 / \8 2 /
$$2 \sqrt{2} \sin^{2}{\left(\frac{20 a + \pi}{8} \right)} \cot{\left(\frac{5 a}{2} + \frac{\pi}{8} \right)}$$
2*sqrt(2)*sin((pi + 20*a)/8)^2*cot(pi/8 + 5*a/2)