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