Parte trigonométrica
[src]
/ 2/15 a\ \
| sec |-- + -| |
| \2 4/ |
4*|1 - -----------------|
| 2/15 pi a\|
| sec |-- - -- + -||
1 \ \2 2 4//
------------- + ----------------------------------------------
/ pi\ / 2/15 a\ \
sec|2*a - --| | sec |-- + -| |
\ 2 / | \2 4/ | /a \ / pi a \
|1 + -----------------|*sec|--|*sec|- -- + --|
| 2/15 pi a\| \26/ \ 2 26/
| sec |-- - -- + -||
\ \2 2 4//
$$\frac{4 \left(- \frac{\sec^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}{\sec^{2}{\left(\frac{a}{4} - \frac{\pi}{2} + \frac{15}{2} \right)}} + 1\right)}{\left(\frac{\sec^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}{\sec^{2}{\left(\frac{a}{4} - \frac{\pi}{2} + \frac{15}{2} \right)}} + 1\right) \sec{\left(\frac{a}{26} \right)} \sec{\left(\frac{a}{26} - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}}$$
/15 11*a\ /15 15*a\
2*tan|-- + ----| 2*tan|-- + ----|
\2 52 / \2 52 /
- ------------------- + ------------------- + sin(2*a)
2/15 11*a\ 2/15 15*a\
1 + tan |-- + ----| 1 + tan |-- + ----|
\2 52 / \2 52 /
$$\sin{\left(2 a \right)} + \frac{2 \tan{\left(\frac{15 a}{52} + \frac{15}{2} \right)}}{\tan^{2}{\left(\frac{15 a}{52} + \frac{15}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{11 a}{52} + \frac{15}{2} \right)}}{\tan^{2}{\left(\frac{11 a}{52} + \frac{15}{2} \right)} + 1}$$
/ pi 11*a\ / pi\ / pi 15*a\
- cos|15 - -- + ----| + cos|2*a - --| + cos|15 - -- + ----|
\ 2 26 / \ 2 / \ 2 26 /
$$\cos{\left(2 a - \frac{\pi}{2} \right)} - \cos{\left(\frac{11 a}{26} - \frac{\pi}{2} + 15 \right)} + \cos{\left(\frac{15 a}{26} - \frac{\pi}{2} + 15 \right)}$$
1 1 1
-------- + -------------- - --------------
csc(2*a) / 15*a\ / 11*a\
csc|15 + ----| csc|15 + ----|
\ 26 / \ 26 /
$$\frac{1}{\csc{\left(\frac{15 a}{26} + 15 \right)}} - \frac{1}{\csc{\left(\frac{11 a}{26} + 15 \right)}} + \frac{1}{\csc{\left(2 a \right)}}$$
/ a\ / pi a \ / pi\
2*cos|15 + -|*cos|- -- + --| + cos|2*a - --|
\ 2/ \ 2 13/ \ 2 /
$$2 \cos{\left(\frac{a}{13} - \frac{\pi}{2} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \cos{\left(2 a - \frac{\pi}{2} \right)}$$
/ a\ / pi a \ / pi\
- 2*cos|15 + -|*cos|- -- - --| + cos|2*a - --|
\ 2/ \ 2 13/ \ 2 /
$$- 2 \cos{\left(- \frac{a}{13} - \frac{\pi}{2} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \cos{\left(2 a - \frac{\pi}{2} \right)}$$
/ 2/15 a\\ /a \
4*|1 - tan |-- + -||*tan|--|
2*tan(a) \ \2 4// \26/
----------- + ---------------------------------
2 / 2/a \\ / 2/15 a\\
1 + tan (a) |1 + tan |--||*|1 + tan |-- + -||
\ \26// \ \2 4//
$$\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \tan{\left(\frac{a}{26} \right)}}{\left(\tan^{2}{\left(\frac{a}{26} \right)} + 1\right) \left(\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1\right)} + \frac{2 \tan{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1}$$
1 2
-------- + -------------------
csc(2*a) /a \ / a\
csc|--|*sec|15 + -|
\13/ \ 2/
$$\frac{1}{\csc{\left(2 a \right)}} + \frac{2}{\csc{\left(\frac{a}{13} \right)} \sec{\left(\frac{a}{2} + 15 \right)}}$$
/ 2/15 a\\ /a \ /a \
4*|1 - tan |-- + -||*cos|--|*sin|--|
\ \2 4// \26/ \26/
------------------------------------ + sin(2*a)
2/15 a\
1 + tan |-- + -|
\2 4/
$$\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \sin{\left(\frac{a}{26} \right)} \cos{\left(\frac{a}{26} \right)}}{\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1} + \sin{\left(2 a \right)}$$
/ 11*a\ / 15*a\
- sin|15 + ----| + sin(2*a) + sin|15 + ----|
\ 26 / \ 26 /
$$\sin{\left(2 a \right)} - \sin{\left(\frac{11 a}{26} + 15 \right)} + \sin{\left(\frac{15 a}{26} + 15 \right)}$$
2
/ 2/a \\ 4/a \ / 2/15 a\\ /a \
4*|1 - tan |--|| *cos |--|*|1 - tan |-- + -||*tan|--|
\ \52// \52/ \ \2 4// \26/
----------------------------------------------------- + sin(2*a)
2/15 a\
1 + tan |-- + -|
\2 4/
$$\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{52} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \cos^{4}{\left(\frac{a}{52} \right)} \tan{\left(\frac{a}{26} \right)}}{\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1} + \sin{\left(2 a \right)}$$
1 2
------------- + --------------------------
/ pi\ / a\ / pi a \
sec|2*a - --| sec|15 + -|*sec|- -- + --|
\ 2 / \ 2/ \ 2 13/
$$\frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}} + \frac{2}{\sec{\left(\frac{a}{13} - \frac{\pi}{2} \right)} \sec{\left(\frac{a}{2} + 15 \right)}}$$
1 2
------------- - --------------------------
/ pi\ / a\ / pi a \
sec|2*a - --| sec|15 + -|*sec|- -- - --|
\ 2 / \ 2/ \ 2 13/
$$\frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}} - \frac{2}{\sec{\left(- \frac{a}{13} - \frac{\pi}{2} \right)} \sec{\left(\frac{a}{2} + 15 \right)}}$$
2
/ 2/a \\ / 1 \
4*|-1 + cot |--|| *|1 - ------------|
\ \52// | 2/15 a\|
| cot |-- + -||
2*cot(a) \ \2 4//
----------- + ------------------------------------------
2 2
1 + cot (a) / 2/a \\ / 1 \ /a \
|1 + cot |--|| *|1 + ------------|*cot|--|
\ \52// | 2/15 a\| \26/
| cot |-- + -||
\ \2 4//
$$\frac{4 \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{52} \right)} - 1\right)^{2}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{52} \right)} + 1\right)^{2} \cot{\left(\frac{a}{26} \right)}} + \frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1}$$
/ 4/15 a\\
| 4*sin |-- + -||
2/a \ 2/pi a \ | \2 4/|
8*sin |--|*sin |-- + --|*|1 - --------------|
\26/ \2 26/ | 2/ a\ |
| sin |15 + -| |
\ \ 2/ /
--------------------------------------------- + sin(2*a)
/ 4/15 a\\
| 4*sin |-- + -||
| \2 4/| /a \
|1 + --------------|*sin|--|
| 2/ a\ | \13/
| sin |15 + -| |
\ \ 2/ /
$$\frac{8 \left(- \frac{4 \sin^{4}{\left(\frac{a}{4} + \frac{15}{2} \right)}}{\sin^{2}{\left(\frac{a}{2} + 15 \right)}} + 1\right) \sin^{2}{\left(\frac{a}{26} \right)} \sin^{2}{\left(\frac{a}{26} + \frac{\pi}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{4} + \frac{15}{2} \right)}}{\sin^{2}{\left(\frac{a}{2} + 15 \right)}} + 1\right) \sin{\left(\frac{a}{13} \right)}} + \sin{\left(2 a \right)}$$
2
/ 2/a \\ / 2/15 a\\ /a \
4*|1 - tan |--|| *|1 - tan |-- + -||*tan|--|
2*tan(a) \ \52// \ \2 4// \26/
----------- + --------------------------------------------
2 2
1 + tan (a) / 2/a \\ / 2/15 a\\
|1 + tan |--|| *|1 + tan |-- + -||
\ \52// \ \2 4//
$$\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{52} \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \tan{\left(\frac{a}{26} \right)}}{\left(\tan^{2}{\left(\frac{a}{52} \right)} + 1\right)^{2} \left(\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1\right)} + \frac{2 \tan{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1}$$
/15 11*a\ /15 15*a\
2*cot|-- + ----| 2*cot|-- + ----|
\2 52 / 2*cot(a) \2 52 /
- ------------------- + ----------- + -------------------
2/15 11*a\ 2 2/15 15*a\
1 + cot |-- + ----| 1 + cot (a) 1 + cot |-- + ----|
\2 52 / \2 52 /
$$\frac{2 \cot{\left(\frac{15 a}{52} + \frac{15}{2} \right)}}{\cot^{2}{\left(\frac{15 a}{52} + \frac{15}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{11 a}{52} + \frac{15}{2} \right)}}{\cot^{2}{\left(\frac{11 a}{52} + \frac{15}{2} \right)} + 1} + \frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1}$$
1 2
-------- + -------------------------
csc(2*a) /a \ / pi a\
csc|--|*csc|-15 + -- - -|
\13/ \ 2 2/
$$\frac{1}{\csc{\left(2 a \right)}} + \frac{2}{\csc{\left(\frac{a}{13} \right)} \csc{\left(- \frac{a}{2} - 15 + \frac{\pi}{2} \right)}}$$
/ 2/ 15 pi a\\
| csc |- -- + -- - -||
| \ 2 2 4/|
4*|1 - -------------------|
| 2/15 a\ |
| csc |-- + -| |
1 \ \2 4/ /
-------- + ----------------------------------------------
csc(2*a) / 2/ 15 pi a\\
| csc |- -- + -- - -||
| \ 2 2 4/| /a \ /pi a \
|1 + -------------------|*csc|--|*csc|-- - --|
| 2/15 a\ | \26/ \2 26/
| csc |-- + -| |
\ \2 4/ /
$$\frac{4 \left(1 - \frac{\csc^{2}{\left(- \frac{a}{4} - \frac{15}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right)}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{4} - \frac{15}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right) \csc{\left(\frac{a}{26} \right)} \csc{\left(- \frac{a}{26} + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(2 a \right)}}$$
/ 2/15 a\\ /a \
4*|-1 + cot |-- + -||*cot|--|
2*cot(a) \ \2 4// \26/
----------- + ---------------------------------
2 / 2/a \\ / 2/15 a\\
1 + cot (a) |1 + cot |--||*|1 + cot |-- + -||
\ \26// \ \2 4//
$$\frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1} + \frac{4 \left(\cot^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} - 1\right) \cot{\left(\frac{a}{26} \right)}}{\left(\cot^{2}{\left(\frac{a}{26} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1\right)}$$
/15 11*a\ /15 15*a\
2*tan|-- + ----| 2*tan|-- + ----|
\2 52 / 2*tan(a) \2 52 /
- ------------------- + ----------- + -------------------
2/15 11*a\ 2 2/15 15*a\
1 + tan |-- + ----| 1 + tan (a) 1 + tan |-- + ----|
\2 52 / \2 52 /
$$\frac{2 \tan{\left(\frac{15 a}{52} + \frac{15}{2} \right)}}{\tan^{2}{\left(\frac{15 a}{52} + \frac{15}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{11 a}{52} + \frac{15}{2} \right)}}{\tan^{2}{\left(\frac{11 a}{52} + \frac{15}{2} \right)} + 1} + \frac{2 \tan{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1}$$
/ 4/30 + a\\
| 8*sin |------||
2/a \ 2/a \ | \ 4 /|
8*cos |--|*sin |--|*|1 - ---------------|
\26/ \26/ \ 1 - cos(30 + a)/
----------------------------------------- + sin(2*a)
/ 4/30 + a\\
| 8*sin |------||
| \ 4 /| /a \
|1 + ---------------|*sin|--|
\ 1 - cos(30 + a)/ \13/
$$\frac{8 \left(1 - \frac{8 \sin^{4}{\left(\frac{a + 30}{4} \right)}}{1 - \cos{\left(a + 30 \right)}}\right) \sin^{2}{\left(\frac{a}{26} \right)} \cos^{2}{\left(\frac{a}{26} \right)}}{\left(1 + \frac{8 \sin^{4}{\left(\frac{a + 30}{4} \right)}}{1 - \cos{\left(a + 30 \right)}}\right) \sin{\left(\frac{a}{13} \right)}} + \sin{\left(2 a \right)}$$
2
/ 2/a \\ 4/a \ / 2/15 a\\ /a \
4*|-1 + cot |--|| *sin |--|*|1 - tan |-- + -||*tan|--|
\ \52// \52/ \ \2 4// \26/
------------------------------------------------------ + sin(2*a)
2/15 a\
1 + tan |-- + -|
\2 4/
$$\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \left(\cot^{2}{\left(\frac{a}{52} \right)} - 1\right)^{2} \sin^{4}{\left(\frac{a}{52} \right)} \tan{\left(\frac{a}{26} \right)}}{\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1} + \sin{\left(2 a \right)}$$
1 1 1
------------- + ------------------- - -------------------
/ pi\ / pi 15*a\ / pi 11*a\
sec|2*a - --| sec|15 - -- + ----| sec|15 - -- + ----|
\ 2 / \ 2 26 / \ 2 26 /
$$\frac{1}{\sec{\left(\frac{15 a}{26} - \frac{\pi}{2} + 15 \right)}} - \frac{1}{\sec{\left(\frac{11 a}{26} - \frac{\pi}{2} + 15 \right)}} + \frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}}$$
/ a\ /a \
2*cos|15 + -|*sin|--| + sin(2*a)
\ 2/ \13/
$$2 \sin{\left(\frac{a}{13} \right)} \cos{\left(\frac{a}{2} + 15 \right)} + \sin{\left(2 a \right)}$$
/ 2/15 pi a\\
| cos |-- - -- + -||
| \2 2 4/| /a \ / pi a \
4*|1 - -----------------|*cos|--|*cos|- -- + --|
| 2/15 a\ | \26/ \ 2 26/
| cos |-- + -| |
\ \2 4/ / / pi\
------------------------------------------------ + cos|2*a - --|
2/15 pi a\ \ 2 /
cos |-- - -- + -|
\2 2 4/
1 + -----------------
2/15 a\
cos |-- + -|
\2 4/
$$\frac{4 \left(1 - \frac{\cos^{2}{\left(\frac{a}{4} - \frac{\pi}{2} + \frac{15}{2} \right)}}{\cos^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}\right) \cos{\left(\frac{a}{26} \right)} \cos{\left(\frac{a}{26} - \frac{\pi}{2} \right)}}{1 + \frac{\cos^{2}{\left(\frac{a}{4} - \frac{\pi}{2} + \frac{15}{2} \right)}}{\cos^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}}} + \cos{\left(2 a - \frac{\pi}{2} \right)}$$
/a \ / pi a\
2*sin|--|*sin|15 + -- + -| + sin(2*a)
\13/ \ 2 2/
$$2 \sin{\left(\frac{a}{13} \right)} \sin{\left(\frac{a}{2} + \frac{\pi}{2} + 15 \right)} + \sin{\left(2 a \right)}$$
2/a \ / 2/15 a\\ /a \
4*cos |--|*|1 - tan |-- + -||*tan|--|
\26/ \ \2 4// \26/
------------------------------------- + sin(2*a)
2/15 a\
1 + tan |-- + -|
\2 4/
$$\frac{4 \left(1 - \tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)}\right) \cos^{2}{\left(\frac{a}{26} \right)} \tan{\left(\frac{a}{26} \right)}}{\tan^{2}{\left(\frac{a}{4} + \frac{15}{2} \right)} + 1} + \sin{\left(2 a \right)}$$
4*cos(a/26)^2*(1 - tan(15/2 + a/4)^2)*tan(a/26)/(1 + tan(15/2 + a/4)^2) + sin(2*a)