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