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