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