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