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