Parte trigonométrica
[src]
2
4 sec (a)
- ------------ + ------------
2/ pi\ 2/ pi\
sec |a - --| sec |a - --|
\ 2 / \ 2 /
-----------------------------
4
-1 + ------------
2/ pi\
sec |a - --|
\ 2 /
$$\frac{\frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{4}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}}{-1 + \frac{4}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}}$$
2/a\
16*tan |-|
2 \2/
tan (a) - --------------
2
/ 2/a\\
|1 + tan |-||
\ \2//
------------------------
2/a\
16*tan |-|
\2/
-1 + --------------
2
/ 2/a\\
|1 + tan |-||
\ \2//
$$\frac{\tan^{2}{\left(a \right)} - \frac{16 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}}{-1 + \frac{16 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}}$$
1 1
-------- - --------
sec(2*a) sec(4*a)
-------------------
1 1
-------- + --------
sec(2*a) sec(4*a)
$$\frac{- \frac{1}{\sec{\left(4 a \right)}} + \frac{1}{\sec{\left(2 a \right)}}}{\frac{1}{\sec{\left(4 a \right)}} + \frac{1}{\sec{\left(2 a \right)}}}$$
1 1
------------- - -------------
/pi \ /pi \
csc|-- - 2*a| csc|-- - 4*a|
\2 / \2 /
-----------------------------
1 1
------------- + -------------
/pi \ /pi \
csc|-- - 4*a| csc|-- - 2*a|
\2 / \2 /
$$\frac{\frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(- 4 a + \frac{\pi}{2} \right)}}}{\frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(- 4 a + \frac{\pi}{2} \right)}}}$$
2/a\
16*cot |-|
1 \2/
------- - --------------
2 2
cot (a) / 2/a\\
|1 + cot |-||
\ \2//
------------------------
2/a\
16*cot |-|
\2/
-1 + --------------
2
/ 2/a\\
|1 + cot |-||
\ \2//
$$\frac{\frac{1}{\cot^{2}{\left(a \right)}} - \frac{16 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}}{-1 + \frac{16 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}}$$
2/ pi\
cos |a - --|
2/ pi\ \ 2 /
- 4*cos |a - --| + ------------
\ 2 / 2
cos (a)
-------------------------------
2/ pi\
-1 + 4*cos |a - --|
\ 2 /
$$\frac{- 4 \cos^{2}{\left(a - \frac{\pi}{2} \right)} + \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}}{4 \cos^{2}{\left(a - \frac{\pi}{2} \right)} - 1}$$
2/pi \
csc |-- - a|
4 \2 /
- ------- + ------------
2 2
csc (a) csc (a)
------------------------
4
-1 + -------
2
csc (a)
$$\frac{\frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}} - \frac{4}{\csc^{2}{\left(a \right)}}}{-1 + \frac{4}{\csc^{2}{\left(a \right)}}}$$
/pi \ /pi \
- sin|-- + 4*a| + sin|-- + 2*a|
\2 / \2 /
-------------------------------
/pi \ /pi \
sin|-- + 2*a| + sin|-- + 4*a|
\2 / \2 /
$$\frac{\sin{\left(2 a + \frac{\pi}{2} \right)} - \sin{\left(4 a + \frac{\pi}{2} \right)}}{\sin{\left(2 a + \frac{\pi}{2} \right)} + \sin{\left(4 a + \frac{\pi}{2} \right)}}$$
2 2
tan (a) - 4*sin (a)
-------------------
2
-1 + 4*sin (a)
$$\frac{- 4 \sin^{2}{\left(a \right)} + \tan^{2}{\left(a \right)}}{4 \sin^{2}{\left(a \right)} - 1}$$
2 2
1 - tan (a) 1 - tan (2*a)
----------- - -------------
2 2
1 + tan (a) 1 + tan (2*a)
---------------------------
2 2
1 - tan (a) 1 - tan (2*a)
----------- + -------------
2 2
1 + tan (a) 1 + tan (2*a)
$$\frac{\frac{1 - \tan^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1} - \frac{1 - \tan^{2}{\left(2 a \right)}}{\tan^{2}{\left(2 a \right)} + 1}}{\frac{1 - \tan^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1} + \frac{1 - \tan^{2}{\left(2 a \right)}}{\tan^{2}{\left(2 a \right)} + 1}}$$
2 2
-1 + cot (a) -1 + cot (2*a)
------------ - --------------
2 2
1 + cot (a) 1 + cot (2*a)
-----------------------------
2 2
-1 + cot (a) -1 + cot (2*a)
------------ + --------------
2 2
1 + cot (a) 1 + cot (2*a)
$$\frac{\frac{\cot^{2}{\left(a \right)} - 1}{\cot^{2}{\left(a \right)} + 1} - \frac{\cot^{2}{\left(2 a \right)} - 1}{\cot^{2}{\left(2 a \right)} + 1}}{\frac{\cot^{2}{\left(a \right)} - 1}{\cot^{2}{\left(a \right)} + 1} + \frac{\cot^{2}{\left(2 a \right)} - 1}{\cot^{2}{\left(2 a \right)} + 1}}$$
4
2 4*sin (a)
- 4*sin (a) + ---------
2
sin (2*a)
-----------------------
2
-1 + 4*sin (a)
$$\frac{\frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} - 4 \sin^{2}{\left(a \right)}}{4 \sin^{2}{\left(a \right)} - 1}$$
(-4*sin(a)^2 + 4*sin(a)^4/sin(2*a)^2)/(-1 + 4*sin(a)^2)