Parte trigonométrica
[src]
/ pi\
cos(x)*sec|x + --|
\ 6 /
$$\cos{\left(x \right)} \sec{\left(x + \frac{\pi}{6} \right)}$$
2
/ 2/x\\ / 1 \ / 1 \
|-1 + cot |-|| *|1 + ------------|*|1 - -------|
\ \4// | 2/x pi\| | 2/x\|
| cot |- + --|| | cot |-||
\ \2 12// \ \2//
------------------------------------------------
2
/ 2/x\\ / 1 \
|1 + cot |-|| *|1 - ------------|
\ \4// | 2/x pi\|
| cot |- + --||
\ \2 12//
$$\frac{\left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2}}{\left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}$$
/ 4/x\\ / 4/x pi\\
| 4*sin |-|| | 4*sin |- + --||
2/pi x\ | \2/| | \2 12/|
sin |-- + -|*|1 - ---------|*|1 + --------------|
\2 2/ | 2 | | 2/ pi\ |
\ sin (x) / | sin |x + --| |
\ \ 6 / /
-------------------------------------------------
4/x pi\
4*sin |- + --|
\2 12/
1 - --------------
2/ pi\
sin |x + --|
\ 6 /
$$\frac{\left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \left(\frac{4 \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(x + \frac{\pi}{6} \right)}} + 1\right) \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}{- \frac{4 \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(x + \frac{\pi}{6} \right)}} + 1}$$
2
/ 2/x\\ 4/x\ / 2/x pi\\ / 2/x\\
|-1 + cot |-|| *sin |-|*|1 + tan |- + --||*|1 - tan |-||
\ \4// \4/ \ \2 12// \ \2//
--------------------------------------------------------
2/x pi\
1 - tan |- + --|
\2 12/
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{x}{4} \right)}}{1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}$$
/ pi\
sec|x + --|
\ 6 /
-----------
sec(x)
$$\frac{\sec{\left(x + \frac{\pi}{6} \right)}}{\sec{\left(x \right)}}$$
/ 2/x 5*pi\\ / 2/x pi\\
| cos |- - ----|| | cos |- - --||
2/x\ | \2 12 /| | \2 2 /|
cos |-|*|1 + --------------|*|1 - ------------|
\2/ | 2/x pi\ | | 2/x\ |
| cos |- + --| | | cos |-| |
\ \2 12/ / \ \2/ /
-----------------------------------------------
2/x 5*pi\
cos |- - ----|
\2 12 /
1 - --------------
2/x pi\
cos |- + --|
\2 12/
$$\frac{\left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \left(\frac{\cos^{2}{\left(\frac{x}{2} - \frac{5 \pi}{12} \right)}}{\cos^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}} + 1\right) \cos^{2}{\left(\frac{x}{2} \right)}}{- \frac{\cos^{2}{\left(\frac{x}{2} - \frac{5 \pi}{12} \right)}}{\cos^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}} + 1}$$
/ 2/x pi\\
| 2*sin |- + --||
2/x\ | \2 12/|
2*cos |-|*|1 + ---------------|*cos(x)
\2/ | / pi\|
| 1 + cos|x + --||
\ \ 6 //
--------------------------------------
/ 2/x pi\\
| 2*sin |- + --||
| \2 12/|
|1 - ---------------|*(1 + cos(x))
| / pi\|
| 1 + cos|x + --||
\ \ 6 //
$$\frac{2 \left(1 + \frac{2 \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}{\cos{\left(x + \frac{\pi}{6} \right)} + 1}\right) \cos^{2}{\left(\frac{x}{2} \right)} \cos{\left(x \right)}}{\left(1 - \frac{2 \sin^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}{\cos{\left(x + \frac{\pi}{6} \right)} + 1}\right) \left(\cos{\left(x \right)} + 1\right)}$$
2/x\ / 2/x pi\\ / 2/x\\
sin |-|*|1 + tan |- + --||*|-1 + cot |-||
\2/ \ \2 3 // \ \2//
-----------------------------------------
/x pi\
2*tan|- + --|
\2 3 /
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{3} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \sin^{2}{\left(\frac{x}{2} \right)}}{2 \tan{\left(\frac{x}{2} + \frac{\pi}{3} \right)}}$$
/ pi\
csc|-x + --|
\ 3 /
------------
/pi \
csc|-- - x|
\2 /
$$\frac{\csc{\left(- x + \frac{\pi}{3} \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}$$
/ pi\
cos(x)*csc|-x + --|
\ 3 /
$$\cos{\left(x \right)} \csc{\left(- x + \frac{\pi}{3} \right)}$$
2/x\ / 2 \
2*cos |-|*|1 + ------------------------------|*cos(x)
\2/ | / / pi\\ 2/x pi\|
| |1 + cos|x + --||*csc |- + --||
\ \ \ 6 // \2 12//
-----------------------------------------------------
/ 2 \
|1 - ------------------------------|*(1 + cos(x))
| / / pi\\ 2/x pi\|
| |1 + cos|x + --||*csc |- + --||
\ \ \ 6 // \2 12//
$$\frac{2 \left(1 + \frac{2}{\left(\cos{\left(x + \frac{\pi}{6} \right)} + 1\right) \csc^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}\right) \cos^{2}{\left(\frac{x}{2} \right)} \cos{\left(x \right)}}{\left(1 - \frac{2}{\left(\cos{\left(x + \frac{\pi}{6} \right)} + 1\right) \csc^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}\right) \left(\cos{\left(x \right)} + 1\right)}$$
/ pi\
sec|x + --|
\ 6 /
-----------
/pi \
csc|-- - x|
\2 /
$$\frac{\sec{\left(x + \frac{\pi}{6} \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}$$
/ 2/x pi\\ / 2/x\\
|1 + cot |- + --||*|-1 + cot |-||
\ \2 12// \ \2//
---------------------------------
/ 2/x\\ / 2/x pi\\
|1 + cot |-||*|-1 + cot |- + --||
\ \2// \ \2 12//
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)} + 1\right)}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)} - 1\right)}$$
/ pi\
sin|x + --|
\ 2 /
-----------
/ pi\
cos|x + --|
\ 6 /
$$\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\cos{\left(x + \frac{\pi}{6} \right)}}$$
/ 2/x pi\ \ / 2/x\ \
| sec |- + --| | | sec |-| |
| \2 12/ | | \2/ |
|1 + --------------|*|1 - ------------|
| 2/x 5*pi\| | 2/x pi\|
| sec |- - ----|| | sec |- - --||
\ \2 12 // \ \2 2 //
---------------------------------------
/ 2/x pi\ \
| sec |- + --| |
| \2 12/ | 2/x\
|1 - --------------|*sec |-|
| 2/x 5*pi\| \2/
| sec |- - ----||
\ \2 12 //
$$\frac{\left(1 + \frac{\sec^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{5 \pi}{12} \right)}}\right) \left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)}{\left(1 - \frac{\sec^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{5 \pi}{12} \right)}}\right) \sec^{2}{\left(\frac{x}{2} \right)}}$$
/ 2/ x 5*pi\\ / 2/pi x\\
| csc |- - + ----|| | csc |-- - -||
| \ 2 12 /| | \2 2/|
|1 + ----------------|*|1 - ------------|
| 2/x pi\ | | 2/x\ |
| csc |- + --| | | csc |-| |
\ \2 12/ / \ \2/ /
-----------------------------------------
/ 2/ x 5*pi\\
| csc |- - + ----||
| \ 2 12 /| 2/pi x\
|1 - ----------------|*csc |-- - -|
| 2/x pi\ | \2 2/
| csc |- + --| |
\ \2 12/ /
$$\frac{\left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \left(\frac{\csc^{2}{\left(- \frac{x}{2} + \frac{5 \pi}{12} \right)}}{\csc^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}} + 1\right)}{\left(- \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{5 \pi}{12} \right)}}{\csc^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}} + 1\right) \csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}$$
2/x\ / 2/x pi\\ / 2/x\\
cos |-|*|1 + tan |- + --||*|1 - tan |-||
\2/ \ \2 12// \ \2//
----------------------------------------
2/x pi\
1 - tan |- + --|
\2 12/
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)} + 1\right) \cos^{2}{\left(\frac{x}{2} \right)}}{1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}$$
/ 4/x\\ / 4/x pi\\
| 4*sin |-|| | 4*sin |- + --||
2/x\ | \2/| | \2 12/|
cos |-|*|1 - ---------|*|1 + --------------|
\2/ | 2 | | 2/ pi\ |
\ sin (x) / | sin |x + --| |
\ \ 6 / /
--------------------------------------------
4/x pi\
4*sin |- + --|
\2 12/
1 - --------------
2/ pi\
sin |x + --|
\ 6 /
$$\frac{\left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \left(\frac{4 \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(x + \frac{\pi}{6} \right)}} + 1\right) \cos^{2}{\left(\frac{x}{2} \right)}}{- \frac{4 \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(x + \frac{\pi}{6} \right)}} + 1}$$
/ 2/x pi\\ / 2/x\\
|1 + tan |- + --||*|-1 + cot |-||
\ \2 3 // \ \2//
---------------------------------
/ 2/x\\ /x pi\
2*|1 + cot |-||*tan|- + --|
\ \2// \2 3 /
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{3} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(\frac{x}{2} + \frac{\pi}{3} \right)}}$$
2
/ 2/x\\ / 2/x pi\\ / 2/x\\
|1 - tan |-|| *|1 + tan |- + --||*|1 - tan |-||
\ \4// \ \2 12// \ \2//
-----------------------------------------------
2
/ 2/x\\ / 2/x pi\\
|1 + tan |-|| *|1 - tan |- + --||
\ \4// \ \2 12//
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)} + 1\right)}{\left(1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}$$
2
/ 2/x\\ 4/x\ / 2/x pi\\ / 2/x\\
|1 - tan |-|| *cos |-|*|1 + tan |- + --||*|1 - tan |-||
\ \4// \4/ \ \2 12// \ \2//
-------------------------------------------------------
2/x pi\
1 - tan |- + --|
\2 12/
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)} + 1\right) \cos^{4}{\left(\frac{x}{4} \right)}}{1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}}$$
/ pi\
sin|x + --|
\ 2 /
-------------
/ 2*pi\
sin|x + ----|
\ 3 /
$$\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\sin{\left(x + \frac{2 \pi}{3} \right)}}$$
/ 2/x pi\\ / 2/x\\
|1 + tan |- + --||*|1 - tan |-||
\ \2 12// \ \2//
--------------------------------
/ 2/x\\ / 2/x pi\\
|1 + tan |-||*|1 - tan |- + --||
\ \2// \ \2 12//
$$\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)} + 1\right)}{\left(1 - \tan^{2}{\left(\frac{x}{2} + \frac{\pi}{12} \right)}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
(1 + tan(x/2 + pi/12)^2)*(1 - tan(x/2)^2)/((1 + tan(x/2)^2)*(1 - tan(x/2 + pi/12)^2))