___ / 2 2 \
\/ 2 *\2 + cot (x) + tan (x)/
-----------------------------
2
2 + (-cot(x) + tan(x))
2 ( tan 2 ( x ) + cot 2 ( x ) + 2 ) ( tan ( x ) − cot ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2} ( tan ( x ) − cot ( x ) ) 2 + 2 2 ( tan 2 ( x ) + cot 2 ( x ) + 2 )
/ 2\
| / I*x -I*x\ |
___ | 2 \- e + e / |
\/ 2 *|2 + cot (x) - -----------------|
| 2 |
| / I*x -I*x\ |
\ \e + e / /
---------------------------------------
2
/ / I*x -I*x\\
| I*\- e + e /|
2 + |-cot(x) + ------------------|
| I*x -I*x |
\ e + e /
2 ( − ( − e i x + e − i x ) 2 ( e i x + e − i x ) 2 + cot 2 ( x ) + 2 ) ( i ( − e i x + e − i x ) e i x + e − i x − cot ( x ) ) 2 + 2 \frac{\sqrt{2} \left(- \frac{\left(- e^{i x} + e^{- i x}\right)^{2}}{\left(e^{i x} + e^{- i x}\right)^{2}} + \cot^{2}{\left(x \right)} + 2\right)}{\left(\frac{i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} - \cot{\left(x \right)}\right)^{2} + 2} ( e i x + e − i x i ( − e i x + e − i x ) − cot ( x ) ) 2 + 2 2 ( − ( e i x + e − i x ) 2 ( − e i x + e − i x ) 2 + cot 2 ( x ) + 2 )
sqrt(2)*(2 + cot(x)^2 - (-exp(i*x) + exp(-i*x))^2/(exp(i*x) + exp(-i*x))^2)/(2 + (-cot(x) + i*(-exp(i*x) + exp(-i*x))/(exp(i*x) + exp(-i*x)))^2)
Parte trigonométrica
[src]
___ / 1 2 \
\/ 2 *|2 + ------- + cot (x)|
| 2 |
\ cot (x) /
-----------------------------
2
/ 1 \
2 + |------ - cot(x)|
\cot(x) /
2 ( cot 2 ( x ) + 2 + 1 cot 2 ( x ) ) ( − cot ( x ) + 1 cot ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\cot^{2}{\left(x \right)} + 2 + \frac{1}{\cot^{2}{\left(x \right)}}\right)}{\left(- \cot{\left(x \right)} + \frac{1}{\cot{\left(x \right)}}\right)^{2} + 2} ( − cot ( x ) + c o t ( x ) 1 ) 2 + 2 2 ( cot 2 ( x ) + 2 + c o t 2 ( x ) 1 )
2
/ 2/pi \\
| csc |-- - x||
___ | \2 /|
\/ 2 *|1 + ------------|
| 2 |
\ csc (x) /
-------------------------
4/pi \
csc |-- - x|
\2 /
1 + ------------
4
csc (x)
2 ( 1 + csc 2 ( − x + π 2 ) csc 2 ( x ) ) 2 1 + csc 4 ( − x + π 2 ) csc 4 ( x ) \frac{\sqrt{2} \left(1 + \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right)^{2}}{1 + \frac{\csc^{4}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{4}{\left(x \right)}}} 1 + c s c 4 ( x ) c s c 4 ( − x + 2 π ) 2 ( 1 + c s c 2 ( x ) c s c 2 ( − x + 2 π ) ) 2
___ / 1 2 \
\/ 2 *|2 + ------- + tan (x)|
| 2 |
\ tan (x) /
-----------------------------
2
/ 1 \
2 + |- ------ + tan(x)|
\ tan(x) /
2 ( tan 2 ( x ) + 2 + 1 tan 2 ( x ) ) ( tan ( x ) − 1 tan ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\tan^{2}{\left(x \right)} + 2 + \frac{1}{\tan^{2}{\left(x \right)}}\right)}{\left(\tan{\left(x \right)} - \frac{1}{\tan{\left(x \right)}}\right)^{2} + 2} ( tan ( x ) − t a n ( x ) 1 ) 2 + 2 2 ( tan 2 ( x ) + 2 + t a n 2 ( x ) 1 )
2
___ / 2 \
\/ 2 *\1 + tan (x)/
--------------------
4
1 + tan (x)
2 ( tan 2 ( x ) + 1 ) 2 tan 4 ( x ) + 1 \frac{\sqrt{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{4}{\left(x \right)} + 1} tan 4 ( x ) + 1 2 ( tan 2 ( x ) + 1 ) 2
___
\/ 2
-------------------------------
4
/ 2/x\\ 4/x\
|1 - tan |-|| 16*tan |-|
\ \2// \2/
-------------- + --------------
4 4
/ 2/x\\ / 2/x\\
|1 + tan |-|| |1 + tan |-||
\ \2// \ \2//
2 ( 1 − tan 2 ( x 2 ) ) 4 ( tan 2 ( x 2 ) + 1 ) 4 + 16 tan 4 ( x 2 ) ( tan 2 ( x 2 ) + 1 ) 4 \frac{\sqrt{2}}{\frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{4}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{4}} + \frac{16 \tan^{4}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{4}}} ( t a n 2 ( 2 x ) + 1 ) 4 ( 1 − t a n 2 ( 2 x ) ) 4 + ( t a n 2 ( 2 x ) + 1 ) 4 16 t a n 4 ( 2 x ) 2
/ 2 2 \
___ | sin (x) cos (x)|
\/ 2 *|2 + ------- + -------|
| 2 2 |
\ cos (x) sin (x)/
-----------------------------
2
/sin(x) cos(x)\
2 + |------ - ------|
\cos(x) sin(x)/
2 ( sin 2 ( x ) cos 2 ( x ) + 2 + cos 2 ( x ) sin 2 ( x ) ) ( sin ( x ) cos ( x ) − cos ( x ) sin ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\frac{\sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right)}{\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + 2} ( c o s ( x ) s i n ( x ) − s i n ( x ) c o s ( x ) ) 2 + 2 2 ( c o s 2 ( x ) s i n 2 ( x ) + 2 + s i n 2 ( x ) c o s 2 ( x ) )
___
\/ 2
-----------------
4 4
cos (x) + sin (x)
2 sin 4 ( x ) + cos 4 ( x ) \frac{\sqrt{2}}{\sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)}} sin 4 ( x ) + cos 4 ( x ) 2
___
\/ 2
----------------------
4 4/ pi\
sin (x) + sin |x + --|
\ 2 /
2 sin 4 ( x ) + sin 4 ( x + π 2 ) \frac{\sqrt{2}}{\sin^{4}{\left(x \right)} + \sin^{4}{\left(x + \frac{\pi}{2} \right)}} sin 4 ( x ) + sin 4 ( x + 2 π ) 2
___
\/ 2
----------------------
1 1
------- + ------------
4 4/pi \
csc (x) csc |-- - x|
\2 /
2 1 csc 4 ( − x + π 2 ) + 1 csc 4 ( x ) \frac{\sqrt{2}}{\frac{1}{\csc^{4}{\left(- x + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{4}{\left(x \right)}}} c s c 4 ( − x + 2 π ) 1 + c s c 4 ( x ) 1 2
2
___ / 1 \
\/ 2 *|1 + -------|
| 2 |
\ cot (x)/
--------------------
1
1 + -------
4
cot (x)
2 ( 1 + 1 cot 2 ( x ) ) 2 1 + 1 cot 4 ( x ) \frac{\sqrt{2} \left(1 + \frac{1}{\cot^{2}{\left(x \right)}}\right)^{2}}{1 + \frac{1}{\cot^{4}{\left(x \right)}}} 1 + c o t 4 ( x ) 1 2 ( 1 + c o t 2 ( x ) 1 ) 2
/ 2/ pi\ \
| cos |x - --| 2 |
___ | \ 2 / cos (x) |
\/ 2 *|2 + ------------ + ------------|
| 2 2/ pi\|
| cos (x) cos |x - --||
\ \ 2 //
---------------------------------------
2
/ / pi\ \
|cos|x - --| |
| \ 2 / cos(x) |
2 + |----------- - -----------|
| cos(x) / pi\|
| cos|x - --||
\ \ 2 //
2 ( cos 2 ( x ) cos 2 ( x − π 2 ) + 2 + cos 2 ( x − π 2 ) cos 2 ( x ) ) ( − cos ( x ) cos ( x − π 2 ) + cos ( x − π 2 ) cos ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\frac{\cos^{2}{\left(x \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)}} + 2 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right)}{\left(- \frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}\right)^{2} + 2} ( − c o s ( x − 2 π ) c o s ( x ) + c o s ( x ) c o s ( x − 2 π ) ) 2 + 2 2 ( c o s 2 ( x − 2 π ) c o s 2 ( x ) + 2 + c o s 2 ( x ) c o s 2 ( x − 2 π ) )
/ 2 2 \
___ | sec (x) csc (x)|
\/ 2 *|2 + ------- + -------|
| 2 2 |
\ csc (x) sec (x)/
-----------------------------
2
/sec(x) csc(x)\
2 + |------ - ------|
\csc(x) sec(x)/
2 ( csc 2 ( x ) sec 2 ( x ) + 2 + sec 2 ( x ) csc 2 ( x ) ) ( − csc ( x ) sec ( x ) + sec ( x ) csc ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\frac{\csc^{2}{\left(x \right)}}{\sec^{2}{\left(x \right)}} + 2 + \frac{\sec^{2}{\left(x \right)}}{\csc^{2}{\left(x \right)}}\right)}{\left(- \frac{\csc{\left(x \right)}}{\sec{\left(x \right)}} + \frac{\sec{\left(x \right)}}{\csc{\left(x \right)}}\right)^{2} + 2} ( − s e c ( x ) c s c ( x ) + c s c ( x ) s e c ( x ) ) 2 + 2 2 ( s e c 2 ( x ) c s c 2 ( x ) + 2 + c s c 2 ( x ) s e c 2 ( x ) )
___
\/ 2
-------------------------------------------
4
/ 2/x\\ 8/x\ 8/x\ 4/x\
|1 - tan |-|| *cos |-| + 16*cos |-|*tan |-|
\ \2// \2/ \2/ \2/
2 ( 1 − tan 2 ( x 2 ) ) 4 cos 8 ( x 2 ) + 16 cos 8 ( x 2 ) tan 4 ( x 2 ) \frac{\sqrt{2}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{4} \cos^{8}{\left(\frac{x}{2} \right)} + 16 \cos^{8}{\left(\frac{x}{2} \right)} \tan^{4}{\left(\frac{x}{2} \right)}} ( 1 − tan 2 ( 2 x ) ) 4 cos 8 ( 2 x ) + 16 cos 8 ( 2 x ) tan 4 ( 2 x ) 2
2
/ 2/ pi\\
| cos |x - --||
___ | \ 2 /|
\/ 2 *|1 + ------------|
| 2 |
\ cos (x) /
-------------------------
4/ pi\
cos |x - --|
\ 2 /
1 + ------------
4
cos (x)
2 ( 1 + cos 2 ( x − π 2 ) cos 2 ( x ) ) 2 1 + cos 4 ( x − π 2 ) cos 4 ( x ) \frac{\sqrt{2} \left(1 + \frac{\cos^{2}{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x \right)}}\right)^{2}}{1 + \frac{\cos^{4}{\left(x - \frac{\pi}{2} \right)}}{\cos^{4}{\left(x \right)}}} 1 + c o s 4 ( x ) c o s 4 ( x − 2 π ) 2 ( 1 + c o s 2 ( x ) c o s 2 ( x − 2 π ) ) 2
2
/ 2 \
___ | sec (x) |
\/ 2 *|1 + ------------|
| 2/ pi\|
| sec |x - --||
\ \ 2 //
-------------------------
4
sec (x)
1 + ------------
4/ pi\
sec |x - --|
\ 2 /
2 ( sec 2 ( x ) sec 2 ( x − π 2 ) + 1 ) 2 sec 4 ( x ) sec 4 ( x − π 2 ) + 1 \frac{\sqrt{2} \left(\frac{\sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 1\right)^{2}}{\frac{\sec^{4}{\left(x \right)}}{\sec^{4}{\left(x - \frac{\pi}{2} \right)}} + 1} s e c 4 ( x − 2 π ) s e c 4 ( x ) + 1 2 ( s e c 2 ( x − 2 π ) s e c 2 ( x ) + 1 ) 2
2
/ 4 \
___ | 4*sin (x)|
\/ 2 *|1 + ---------|
| 2 |
\ sin (2*x)/
----------------------
8
16*sin (x)
1 + ----------
4
sin (2*x)
2 ( 4 sin 4 ( x ) sin 2 ( 2 x ) + 1 ) 2 16 sin 8 ( x ) sin 4 ( 2 x ) + 1 \frac{\sqrt{2} \left(\frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 1\right)^{2}}{\frac{16 \sin^{8}{\left(x \right)}}{\sin^{4}{\left(2 x \right)}} + 1} s i n 4 ( 2 x ) 16 s i n 8 ( x ) + 1 2 ( s i n 2 ( 2 x ) 4 s i n 4 ( x ) + 1 ) 2
___
\/ 2
---------------------
/ 4 \ 4
\1 + tan (x)/*cos (x)
2 ( tan 4 ( x ) + 1 ) cos 4 ( x ) \frac{\sqrt{2}}{\left(\tan^{4}{\left(x \right)} + 1\right) \cos^{4}{\left(x \right)}} ( tan 4 ( x ) + 1 ) cos 4 ( x ) 2
___
\/ 2
--------------------------------------------
4
/ 2/x\\ 8/x\ 4/x\ 8/x\
|-1 + cot |-|| *sin |-| + 16*cot |-|*sin |-|
\ \2// \2/ \2/ \2/
2 ( cot 2 ( x 2 ) − 1 ) 4 sin 8 ( x 2 ) + 16 sin 8 ( x 2 ) cot 4 ( x 2 ) \frac{\sqrt{2}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{x}{2} \right)} + 16 \sin^{8}{\left(\frac{x}{2} \right)} \cot^{4}{\left(\frac{x}{2} \right)}} ( cot 2 ( 2 x ) − 1 ) 4 sin 8 ( 2 x ) + 16 sin 8 ( 2 x ) cot 4 ( 2 x ) 2
___
\/ 2
----------------------
4 4/ pi\
cos (x) + cos |x - --|
\ 2 /
2 cos 4 ( x ) + cos 4 ( x − π 2 ) \frac{\sqrt{2}}{\cos^{4}{\left(x \right)} + \cos^{4}{\left(x - \frac{\pi}{2} \right)}} cos 4 ( x ) + cos 4 ( x − 2 π ) 2
/ 4 2 \
___ | 4*sin (x) sin (2*x)|
\/ 2 *|2 + --------- + ---------|
| 2 4 |
\ sin (2*x) 4*sin (x)/
---------------------------------
2
/ 2 \
|2*sin (x) sin(2*x)|
2 + |--------- - ---------|
| sin(2*x) 2 |
\ 2*sin (x)/
2 ( 4 sin 4 ( x ) sin 2 ( 2 x ) + 2 + sin 2 ( 2 x ) 4 sin 4 ( x ) ) ( 2 sin 2 ( x ) sin ( 2 x ) − sin ( 2 x ) 2 sin 2 ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\frac{4 \sin^{4}{\left(x \right)}}{\sin^{2}{\left(2 x \right)}} + 2 + \frac{\sin^{2}{\left(2 x \right)}}{4 \sin^{4}{\left(x \right)}}\right)}{\left(\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}} - \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}\right)^{2} + 2} ( s i n ( 2 x ) 2 s i n 2 ( x ) − 2 s i n 2 ( x ) s i n ( 2 x ) ) 2 + 2 2 ( s i n 2 ( 2 x ) 4 s i n 4 ( x ) + 2 + 4 s i n 4 ( x ) s i n 2 ( 2 x ) )
/ 2/pi \ \
| csc |-- - x| 2 |
___ | \2 / csc (x) |
\/ 2 *|2 + ------------ + ------------|
| 2 2/pi \|
| csc (x) csc |-- - x||
\ \2 //
---------------------------------------
2
/ /pi \ \
|csc|-- - x| |
| \2 / csc(x) |
2 + |----------- - -----------|
| csc(x) /pi \|
| csc|-- - x||
\ \2 //
2 ( csc 2 ( x ) csc 2 ( − x + π 2 ) + 2 + csc 2 ( − x + π 2 ) csc 2 ( x ) ) ( − csc ( x ) csc ( − x + π 2 ) + csc ( − x + π 2 ) csc ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\frac{\csc^{2}{\left(x \right)}}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} + 2 + \frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{\csc^{2}{\left(x \right)}}\right)}{\left(- \frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}\right)^{2} + 2} ( − c s c ( − x + 2 π ) c s c ( x ) + c s c ( x ) c s c ( − x + 2 π ) ) 2 + 2 2 ( c s c 2 ( − x + 2 π ) c s c 2 ( x ) + 2 + c s c 2 ( x ) c s c 2 ( − x + 2 π ) )
___
\/ 2
----------------------
1 1
------- + ------------
4 4/ pi\
sec (x) sec |x - --|
\ 2 /
2 1 sec 4 ( x − π 2 ) + 1 sec 4 ( x ) \frac{\sqrt{2}}{\frac{1}{\sec^{4}{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec^{4}{\left(x \right)}}} s e c 4 ( x − 2 π ) 1 + s e c 4 ( x ) 1 2
/ 2/ pi\ \
| sec |x - --| 2 |
___ | \ 2 / sec (x) |
\/ 2 *|2 + ------------ + ------------|
| 2 2/ pi\|
| sec (x) sec |x - --||
\ \ 2 //
---------------------------------------
2
/ / pi\\
| sec|x - --||
| sec(x) \ 2 /|
2 + |----------- - -----------|
| / pi\ sec(x) |
|sec|x - --| |
\ \ 2 / /
2 ( sec 2 ( x ) sec 2 ( x − π 2 ) + 2 + sec 2 ( x − π 2 ) sec 2 ( x ) ) ( sec ( x ) sec ( x − π 2 ) − sec ( x − π 2 ) sec ( x ) ) 2 + 2 \frac{\sqrt{2} \left(\frac{\sec^{2}{\left(x \right)}}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + 2 + \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{\sec^{2}{\left(x \right)}}\right)}{\left(\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}} - \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}\right)^{2} + 2} ( s e c ( x − 2 π ) s e c ( x ) − s e c ( x ) s e c ( x − 2 π ) ) 2 + 2 2 ( s e c 2 ( x − 2 π ) s e c 2 ( x ) + 2 + s e c 2 ( x ) s e c 2 ( x − 2 π ) )
___
\/ 2
--------------------------------
4
/ 2/x\\ 4/x\
|-1 + cot |-|| 16*cot |-|
\ \2// \2/
--------------- + --------------
4 4
/ 2/x\\ / 2/x\\
|1 + cot |-|| |1 + cot |-||
\ \2// \ \2//
2 ( cot 2 ( x 2 ) − 1 ) 4 ( cot 2 ( x 2 ) + 1 ) 4 + 16 cot 4 ( x 2 ) ( cot 2 ( x 2 ) + 1 ) 4 \frac{\sqrt{2}}{\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{4}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{4}} + \frac{16 \cot^{4}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{4}}} ( c o t 2 ( 2 x ) + 1 ) 4 ( c o t 2 ( 2 x ) − 1 ) 4 + ( c o t 2 ( 2 x ) + 1 ) 4 16 c o t 4 ( 2 x ) 2
sqrt(2)/((-1 + cot(x/2)^2)^4/(1 + cot(x/2)^2)^4 + 16*cot(x/2)^4/(1 + cot(x/2)^2)^4)