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