Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cot(pi/(2-a))*(-sin(a-3*pi/2)-sin(a))/((cot(a)*(cos(a)-(-1)*sin(a))))
¿Cómo vas a descomponer esta cot(pi/(2-a))*(-sin(a-3*pi/2)-sin(a))/((cot(a)*(cos(a)-(-1)*sin(a)))) expresión en fracciones?
Solución
Ha introducido
[src]
/ pi \ / / 3*pi\ \
cot|-----|*|- sin|a - ----| - sin(a)|
\2 - a/ \ \ 2 / /
-------------------------------------
cot(a)*(cos(a) + sin(a))
$$\frac{\left(- \sin{\left(a \right)} - \sin{\left(a - \frac{3 \pi}{2} \right)}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \cot{\left(a \right)}}$$
(cot(pi/(2 - a))*(-sin(a - 3*pi/2) - sin(a)))/((cot(a)*(cos(a) + sin(a))))
Simplificación general
[src]
/ pi \ cot|------|*tan(a) \-2 + a/
$$\tan{\left(a \right)} \cot{\left(\frac{\pi}{a - 2} \right)}$$
cot(pi/(-2 + a))*tan(a)
Denominador común
[src]
/ pi \
-cot|-----|
\2 - a/
------------
cot(a)
$$- \frac{\cot{\left(\frac{\pi}{2 - a} \right)}}{\cot{\left(a \right)}}$$
-cot(pi/(2 - a))/cot(a)
Unión de expresiones racionales
[src]
/ /-3*pi + 2*a\\ / pi \
|-sin(a) - sin|-----------||*cot|-----|
\ \ 2 // \2 - a/
---------------------------------------
(cos(a) + sin(a))*cot(a)
$$\frac{\left(- \sin{\left(a \right)} - \sin{\left(\frac{2 a - 3 \pi}{2} \right)}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \cot{\left(a \right)}}$$
(-sin(a) - sin((-3*pi + 2*a)/2))*cot(pi/(2 - a))/((cos(a) + sin(a))*cot(a))
Denominador racional
[src]
/ pi \ cot|------| \-2 + a/ ----------- cot(a)
$$\frac{\cot{\left(\frac{\pi}{a - 2} \right)}}{\cot{\left(a \right)}}$$
cot(pi/(-2 + a))/cot(a)
Combinatoria
[src]
/ pi \
-cot|-----|
\2 - a/
------------
cot(a)
$$- \frac{\cot{\left(\frac{\pi}{2 - a} \right)}}{\cot{\left(a \right)}}$$
-cot(pi/(2 - a))/cot(a)
Respuesta numérica
[src]
(-sin(a) - sin(a - 3*pi/2))*cot(pi/(2 - a))/((cos(a) + sin(a))*cot(a))
(-sin(a) - sin(a - 3*pi/2))*cot(pi/(2 - a))/((cos(a) + sin(a))*cot(a))
Parte trigonométrica
[src]
/ /pi \\
| csc|-- - a||
___ | \2 /| / pi \ / pi\
\/ 2 *|1 + -----------|*csc|------|*csc|a + --|
\ csc(a) / \-2 + a/ \ 4 /
-----------------------------------------------
/pi pi \
2*csc(a)*csc|-- - ------|
\2 -2 + a/
$$\frac{\sqrt{2} \left(1 + \frac{\csc{\left(- a + \frac{\pi}{2} \right)}}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{a - 2} \right)} \csc{\left(a + \frac{\pi}{4} \right)}}{2 \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a - 2} \right)}}$$
/ pi \ / pi\
cos|------|*cos|a - --|
\-2 + a/ \ 2 /
-------------------------
/ pi pi \
cos(a)*cos|- -- + ------|
\ 2 -2 + a/
$$\frac{\cos{\left(\frac{\pi}{a - 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)}}$$
/ pi \ cot|------|*tan(a) \-2 + a/
$$\tan{\left(a \right)} \cot{\left(\frac{\pi}{a - 2} \right)}$$
/ / 1 \ /a pi\\
| |1 + ------|*csc|- + --||
___ | 1 \ csc(a)/ \2 4 /| / pi \ / pi\ /pi \
\/ 2 *|- ------ - ------------------------|*csc|-----|*csc|a + --|*csc|-- - a|
| csc(a) / a pi\ | \2 - a/ \ 4 / \2 /
| csc|- - + --| |
\ \ 2 4 / /
------------------------------------------------------------------------------
/pi pi \
2*csc(a)*csc|-- - -----|
\2 2 - a/
$$\frac{\sqrt{2} \left(- \frac{\left(1 + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\csc{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{2 - a} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc{\left(a + \frac{\pi}{4} \right)}}{2 \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{2 - a} \right)}}$$
/ pi pi \
sec(a)*sec|- -- + ------|
\ 2 -2 + a/
-------------------------
/ pi \ / pi\
sec|------|*sec|a - --|
\-2 + a/ \ 2 /
$$\frac{\sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)}}{\sec{\left(\frac{\pi}{a - 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
/ pi \ cot|------| \-2 + a/ ----------- cot(a)
$$\frac{\cot{\left(\frac{\pi}{a - 2} \right)}}{\cot{\left(a \right)}}$$
/ / / pi\\ /a pi\\
| |1 + cos|a - --||*cos|- + --||
___ | / pi\ \ \ 2 // \2 4 /| / pi \ / pi\
\/ 2 *|- cos|a - --| - -----------------------------|*cos|-----|*cos|a - --|
| \ 2 / /a pi\ | \2 - a/ \ 2 /
| cos|- - --| |
\ \2 4 / /
----------------------------------------------------------------------------
/ pi\ / pi pi \
2*cos(a)*cos|a - --|*cos|- -- + -----|
\ 4 / \ 2 2 - a/
$$\frac{\sqrt{2} \left(- \frac{\left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos{\left(\frac{a}{2} - \frac{\pi}{4} \right)}} - \cos{\left(a - \frac{\pi}{2} \right)}\right) \cos{\left(\frac{\pi}{2 - a} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{2 \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)} \cos{\left(a - \frac{\pi}{4} \right)}}$$
/ 2 \
___ | /a\ 2*sin (a) |
\/ 2 *|- tan(a)*tan|-| + --------- + tan(a)|
\ \2/ cos(a) /
--------------------------------------------
/ /a\\ / pi\ / pi \
2*|1 + tan|-||*sin|a + --|*tan|------|
\ \2// \ 4 / \-2 + a/
$$\frac{\sqrt{2} \left(\frac{2 \sin^{2}{\left(a \right)}}{\cos{\left(a \right)}} - \tan{\left(\frac{a}{2} \right)} \tan{\left(a \right)} + \tan{\left(a \right)}\right)}{2 \left(\tan{\left(\frac{a}{2} \right)} + 1\right) \sin{\left(a + \frac{\pi}{4} \right)} \tan{\left(\frac{\pi}{a - 2} \right)}}$$
/ pi \ /pi \
csc|------|*csc|-- - a|
\-2 + a/ \2 /
-----------------------
/pi pi \
csc(a)*csc|-- - ------|
\2 -2 + a/
$$\frac{\csc{\left(\frac{\pi}{a - 2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}{\csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{a - 2} \right)}}$$
___ 2 / (1 + sin(a))*cos(a)\ / 2*pi\
\/ 2 *sin (a)*|-sin(a) - -------------------|*sin|-----|
| 2/a pi\ | \2 - a/
| 2*sin |- + --| |
\ \2 4 / /
--------------------------------------------------------
2/ pi \ / pi\
2*sin(2*a)*sin |-----|*sin|a + --|
\2 - a/ \ 4 /
$$\frac{\sqrt{2} \left(- \frac{\left(\sin{\left(a \right)} + 1\right) \cos{\left(a \right)}}{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - \sin{\left(a \right)}\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{2 \pi}{2 - a} \right)}}{2 \sin{\left(2 a \right)} \sin^{2}{\left(\frac{\pi}{2 - a} \right)} \sin{\left(a + \frac{\pi}{4} \right)}}$$
/ pi \
(-cos(a) - sin(a))*cos|-----|*sin(a)
\2 - a/
------------------------------------
/ pi \
(cos(a) + sin(a))*cos(a)*sin|-----|
\2 - a/
$$\frac{\left(- \sin{\left(a \right)} - \cos{\left(a \right)}\right) \sin{\left(a \right)} \cos{\left(\frac{\pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \sin{\left(\frac{\pi}{2 - a} \right)} \cos{\left(a \right)}}$$
/ 2 \
___ | /a\ 2*sin (a)|
-\/ 2 *|-tan(a) + tan(a)*tan|-| - ---------|
\ \2/ cos(a) /
---------------------------------------------
/ /a\\ / pi\ / pi \
2*|1 + tan|-||*sin|a + --|*tan|------|
\ \2// \ 4 / \-2 + a/
$$- \frac{\sqrt{2} \left(- \frac{2 \sin^{2}{\left(a \right)}}{\cos{\left(a \right)}} + \tan{\left(\frac{a}{2} \right)} \tan{\left(a \right)} - \tan{\left(a \right)}\right)}{2 \left(\tan{\left(\frac{a}{2} \right)} + 1\right) \sin{\left(a + \frac{\pi}{4} \right)} \tan{\left(\frac{\pi}{a - 2} \right)}}$$
___ / 2/a pi\\ / /a\\
\/ 2 *|1 + tan |- + --||*|-1 - 2*sin(a) + tan|-||*tan(a)
\ \2 8 // \ \2//
--------------------------------------------------------
/ /a\\ / pi \ /a pi\
4*|1 + tan|-||*tan|-----|*tan|- + --|
\ \2// \2 - a/ \2 8 /
$$\frac{\sqrt{2} \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \left(- 2 \sin{\left(a \right)} + \tan{\left(\frac{a}{2} \right)} - 1\right) \tan{\left(a \right)}}{4 \left(\tan{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{\pi}{2 - a} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}$$
___ / sin(a) \ / 2*pi \
\/ 2 *|1 + -----------|*sin(a)*sin|------|
| / pi\| \-2 + a/
| sin|a + --||
\ \ 2 //
------------------------------------------
2/ pi \ / pi\
4*sin |------|*sin|a + --|
\-2 + a/ \ 4 /
$$\frac{\sqrt{2} \left(\frac{\sin{\left(a \right)}}{\sin{\left(a + \frac{\pi}{2} \right)}} + 1\right) \sin{\left(a \right)} \sin{\left(\frac{2 \pi}{a - 2} \right)}}{4 \sin^{2}{\left(\frac{\pi}{a - 2} \right)} \sin{\left(a + \frac{\pi}{4} \right)}}$$
2 / 2*pi \
sin (a)*sin|------|
\-2 + a/
---------------------
2/ pi \
sin(2*a)*sin |------|
\-2 + a/
$$\frac{\sin^{2}{\left(a \right)} \sin{\left(\frac{2 \pi}{a - 2} \right)}}{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{\pi}{a - 2} \right)}}$$
/ /a\ /a pi\ \
| 2*cot|-| 2*cot|- + --| |
| \2/ \2 4 / | / pi \
|- ----------- - ----------------|*cot|-----|
| 2/a\ 2/a pi\| \2 - a/
| 1 + cot |-| 1 + cot |- + --||
\ \2/ \2 4 //
---------------------------------------------
/ 2/a\ /a\ \
|-1 + cot |-| 2*cot|-| |
| \2/ \2/ |
|------------ + -----------|*cot(a)
| 2/a\ 2/a\|
|1 + cot |-| 1 + cot |-||
\ \2/ \2//
$$\frac{\left(- \frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \cot{\left(a \right)}}$$
2 / 2*pi\
sin (a)*(-cos(a) - sin(a))*sin|-----|
\2 - a/
-------------------------------------------
/ / pi\\ 2/ pi \
|sin(a) + sin|a + --||*sin(2*a)*sin |-----|
\ \ 2 // \2 - a/
$$\frac{\left(- \sin{\left(a \right)} - \cos{\left(a \right)}\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{2 \pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \sin{\left(a + \frac{\pi}{2} \right)}\right) \sin{\left(2 a \right)} \sin^{2}{\left(\frac{\pi}{2 - a} \right)}}$$
/ / pi\\ / pi \ / pi\ |-cos(a - 2*pi) - cos|a - --||*cos|-----|*cos|a - --| \ \ 2 // \2 - a/ \ 2 / ----------------------------------------------------- / / pi\\ / pi pi \ |cos(a) + cos|a - --||*cos(a)*cos|- -- + -----| \ \ 2 // \ 2 2 - a/
$$\frac{\left(- \cos{\left(a - 2 \pi \right)} - \cos{\left(a - \frac{\pi}{2} \right)}\right) \cos{\left(\frac{\pi}{2 - a} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{\left(\cos{\left(a \right)} + \cos{\left(a - \frac{\pi}{2} \right)}\right) \cos{\left(a \right)} \cos{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)}}$$
/ /a\ \
| 2*tan|-| |
___ / 2/a pi\\ | \2/ | /a\
\/ 2 *|1 + tan |- + --||*|1 + -----------|*tan|-|
\ \2 8 // | 2/a\| \2/
| 1 - tan |-||
\ \2//
-------------------------------------------------
/ 2/a\\ / pi \ /a pi\
2*|1 + tan |-||*tan|------|*tan|- + --|
\ \2// \-2 + a/ \2 8 /
$$\frac{\sqrt{2} \left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{1 - \tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)}}{2 \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(\frac{\pi}{a - 2} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}$$
/ /a\ \
| 2*tan|-| |
| \2/ |
| 1 + ----------- |
| 2/a\ /a\ |
| 1 + tan |-| 2*tan|-| |
___ / 2/a pi\\ | \2/ \2/ |
\/ 2 *|1 + tan |- + --||*|- --------------- - -----------|*tan(a)
\ \2 8 // | /a pi\ 2/a\|
| tan|- + --| 1 + tan |-||
\ \2 4 / \2//
-----------------------------------------------------------------
/ pi \ /a pi\
4*tan|-----|*tan|- + --|
\2 - a/ \2 8 /
$$\frac{\sqrt{2} \left(- \frac{1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}}{\tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \tan{\left(a \right)}}{4 \tan{\left(\frac{\pi}{2 - a} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}$$
___ / sec(a) \ / pi\ / pi pi \
\/ 2 *|1 + -----------|*sec|a - --|*sec|- -- + ------|
| / pi\| \ 4 / \ 2 -2 + a/
| sec|a - --||
\ \ 2 //
------------------------------------------------------
/ pi \ / pi\
2*sec|------|*sec|a - --|
\-2 + a/ \ 2 /
$$\frac{\sqrt{2} \left(\frac{\sec{\left(a \right)}}{\sec{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)} \sec{\left(a - \frac{\pi}{4} \right)}}{2 \sec{\left(\frac{\pi}{a - 2} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
/ /a\ \
| 2*cot|-| |
___ / 2/a pi\\ | \2/ | /a\ / pi \
\/ 2 *|1 + cot |- + --||*|1 + ------------|*cot|-|*cot|------|
\ \2 8 // | 2/a\| \2/ \-2 + a/
| -1 + cot |-||
\ \2//
--------------------------------------------------------------
/ 2/a\\ /a pi\
2*|1 + cot |-||*cot|- + --|
\ \2// \2 8 /
$$\frac{\sqrt{2} \left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} - 1}\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{\pi}{a - 2} \right)}}{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}$$
/ pi \
-cot|-----|*tan(a)
\2 - a/
$$- \tan{\left(a \right)} \cot{\left(\frac{\pi}{2 - a} \right)}$$
/ / pi\\
| cos|a - --||
___ | \ 2 /| / pi \ / pi\
\/ 2 *|1 + -----------|*cos|------|*cos|a - --|
\ cos(a) / \-2 + a/ \ 2 /
-----------------------------------------------
/ pi\ / pi pi \
2*cos|a - --|*cos|- -- + ------|
\ 4 / \ 2 -2 + a/
$$\frac{\sqrt{2} \left(1 + \frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\cos{\left(a \right)}}\right) \cos{\left(\frac{\pi}{a - 2} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{2 \cos{\left(- \frac{\pi}{2} + \frac{\pi}{a - 2} \right)} \cos{\left(a - \frac{\pi}{4} \right)}}$$
/ 1 1 \ / pi pi \
|- ------------- - -----------|*sec(a)*sec|- -- + -----|
| sec(a - 2*pi) / pi\| \ 2 2 - a/
| sec|a - --||
\ \ 2 //
--------------------------------------------------------
/ 1 1 \ / pi \ / pi\
|------ + -----------|*sec|-----|*sec|a - --|
|sec(a) / pi\| \2 - a/ \ 2 /
| sec|a - --||
\ \ 2 //
$$\frac{\left(- \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(a - 2 \pi \right)}}\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)}}{\left(\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(a \right)}}\right) \sec{\left(\frac{\pi}{2 - a} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
___ 2/a\ /a\ / pi \ /a pi\
\/ 2 *sin |-|*(1 + tan(a))*cot|-|*cot|------|*tan|- + --|
\2/ \2/ \-2 + a/ \2 8 /
---------------------------------------------------------
2/a pi\
2*sin |- + --|
\2 8 /
$$\frac{\sqrt{2} \left(\tan{\left(a \right)} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)} \cot{\left(\frac{a}{2} \right)} \cot{\left(\frac{\pi}{a - 2} \right)}}{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}$$
/ 1 1 \ / pi \ /pi \ |- ------ - ------|*csc|-----|*csc|-- - a| \ csc(a) sec(a)/ \2 - a/ \2 / --------------------------------------------- / 1 1 \ /pi pi \ |------ + -----------|*csc(a)*csc|-- - -----| |csc(a) /pi \| \2 2 - a/ | csc|-- - a|| \ \2 //
$$\frac{\left(- \frac{1}{\sec{\left(a \right)}} - \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{2 - a} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}{\left(\frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(a \right)} \csc{\left(\frac{\pi}{2} - \frac{\pi}{2 - a} \right)}}$$
/ / 1 \ /a pi\\
| |1 + -----------|*sec|- - --||
| | / pi\| \2 4 /|
| | sec|a - --|| |
___ | 1 \ \ 2 // | / pi\ / pi pi \
\/ 2 *|- ----------- - -----------------------------|*sec(a)*sec|a - --|*sec|- -- + -----|
| / pi\ /a pi\ | \ 4 / \ 2 2 - a/
| sec|a - --| sec|- + --| |
\ \ 2 / \2 4 / /
------------------------------------------------------------------------------------------
/ pi \ / pi\
2*sec|-----|*sec|a - --|
\2 - a/ \ 2 /
$$\frac{\sqrt{2} \left(- \frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\sec{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec{\left(a \right)} \sec{\left(- \frac{\pi}{2} + \frac{\pi}{2 - a} \right)} \sec{\left(a - \frac{\pi}{4} \right)}}{2 \sec{\left(\frac{\pi}{2 - a} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
/ 1 1 \ / pi \ |- ------ - -----------|*csc|-----|*sec(a) | csc(a) /pi \| \2 - a/ | csc|-- - a|| \ \2 // ------------------------------------------ / 1 1 \ / pi \ |------ + ------|*csc(a)*sec|-----| \csc(a) sec(a)/ \2 - a/
$$\frac{\left(- \frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{2 - a} \right)} \sec{\left(a \right)}}{\left(\frac{1}{\sec{\left(a \right)}} + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(a \right)} \sec{\left(\frac{\pi}{2 - a} \right)}}$$
/ 1 1 \ / pi \ |- ------ - ------|*csc|-----|*sec(a) \ csc(a) sec(a)/ \2 - a/ ------------------------------------- / 1 1 \ / pi \ |------ + ------|*csc(a)*sec|-----| \csc(a) sec(a)/ \2 - a/
$$\frac{\left(- \frac{1}{\sec{\left(a \right)}} - \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(\frac{\pi}{2 - a} \right)} \sec{\left(a \right)}}{\left(\frac{1}{\sec{\left(a \right)}} + \frac{1}{\csc{\left(a \right)}}\right) \csc{\left(a \right)} \sec{\left(\frac{\pi}{2 - a} \right)}}$$
/ / /a\ \ /a\ \
| | 2*cot|-| | 2*cot|-| |
___ / 2/a pi\\ | | \2/ | /a pi\ \2/ | / pi \
\/ 2 *|1 + cot |- + --||*|- |1 + -----------|*cot|- + --| - -----------|*cot|-----|
\ \2 8 // | | 2/a\| \2 4 / 2/a\| \2 - a/
| | 1 + cot |-|| 1 + cot |-||
\ \ \2// \2//
-----------------------------------------------------------------------------------
/a pi\
4*cot(a)*cot|- + --|
\2 8 /
$$\frac{\sqrt{2} \left(- \left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{4 \cot{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}$$
___ / /a pi\\ / pi \
\/ 2 *|-sin(a) - (1 + sin(a))*cot|- + --||*cot|-----|*tan(a)
\ \2 4 // \2 - a/
------------------------------------------------------------
/ pi\
2*sin|a + --|
\ 4 /
$$\frac{\sqrt{2} \left(- \left(\sin{\left(a \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - \sin{\left(a \right)}\right) \tan{\left(a \right)} \cot{\left(\frac{\pi}{2 - a} \right)}}{2 \sin{\left(a + \frac{\pi}{4} \right)}}$$
___ / sin(a)\
\/ 2 *|1 + ------|*sin(a)
\ cos(a)/
-------------------------
/ pi\ / pi \
2*sin|a + --|*tan|------|
\ 4 / \-2 + a/
$$\frac{\sqrt{2} \left(\frac{\sin{\left(a \right)}}{\cos{\left(a \right)}} + 1\right) \sin{\left(a \right)}}{2 \sin{\left(a + \frac{\pi}{4} \right)} \tan{\left(\frac{\pi}{a - 2} \right)}}$$
tan(a) ----------- / pi \ tan|------| \-2 + a/
$$\frac{\tan{\left(a \right)}}{\tan{\left(\frac{\pi}{a - 2} \right)}}$$
/ /a\ /a pi\ \ | 2*tan|-| 2*tan|- + --| | | \2/ \2 4 / | |- ----------- - ----------------|*tan(a) | 2/a\ 2/a pi\| | 1 + tan |-| 1 + tan |- + --|| \ \2/ \2 4 // ----------------------------------------- / 2/a\ /a\ \ |1 - tan |-| 2*tan|-| | | \2/ \2/ | / pi \ |----------- + -----------|*tan|-----| | 2/a\ 2/a\| \2 - a/ |1 + tan |-| 1 + tan |-|| \ \2/ \2//
$$\frac{\left(- \frac{2 \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \tan{\left(a \right)}}{\left(\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \tan{\left(\frac{\pi}{2 - a} \right)}}$$
___ 2/a\ / 2/a pi\\ /a\
\/ 2 *cos |-|*|1 + tan |- + --||*(1 + tan(a))*tan|-|
\2/ \ \2 8 // \2/
----------------------------------------------------
/ pi \ /a pi\
2*tan|------|*tan|- + --|
\-2 + a/ \2 8 /
$$\frac{\sqrt{2} \left(\tan{\left(a \right)} + 1\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)}}{2 \tan{\left(\frac{\pi}{a - 2} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}$$
2 / / pi\\ / 2*pi\
sin (a)*|-sin(a) - sin|a + --||*sin|-----|
\ \ 2 // \2 - a/
------------------------------------------
2/ pi \
(cos(a) + sin(a))*sin(2*a)*sin |-----|
\2 - a/
$$\frac{\left(- \sin{\left(a \right)} - \sin{\left(a + \frac{\pi}{2} \right)}\right) \sin^{2}{\left(a \right)} \sin{\left(\frac{2 \pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \sin{\left(2 a \right)} \sin^{2}{\left(\frac{\pi}{2 - a} \right)}}$$
___ / /a pi\\ / pi \ /a pi\
\/ 2 *|-sin(a) - (1 + sin(a))*cot|- + --||*cot|-----|*tan(a)*tan|- + --|
\ \2 4 // \2 - a/ \2 8 /
------------------------------------------------------------------------
2/a pi\
4*sin |- + --|
\2 8 /
$$\frac{\sqrt{2} \left(- \left(\sin{\left(a \right)} + 1\right) \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - \sin{\left(a \right)}\right) \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{8} \right)} \cot{\left(\frac{\pi}{2 - a} \right)}}{4 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{8} \right)}}$$
sqrt(2)*(-sin(a) - (1 + sin(a))*cot(a/2 + pi/4))*cot(pi/(2 - a))*tan(a)*tan(a/2 + pi/8)/(4*sin(a/2 + pi/8)^2)
Potencias
[src]
/ / / 3*pi\ / 3*pi\\ \
| | I*|-a + ----| I*|a - ----|| |
| | \ 2 / \ 2 /| / -I*a I*a\|
|I*\- e + e / I*\- e + e /| / pi \
|------------------------------------ + ------------------|*cot|-----|
\ 2 2 / \2 - a/
----------------------------------------------------------------------
/ I*a -I*a / -I*a I*a\\
|e e I*\- e + e /|
|---- + ----- - ------------------|*cot(a)
\ 2 2 2 /
$$\frac{\left(\frac{i \left(e^{i a} - e^{- i a}\right)}{2} + \frac{i \left(- e^{i \left(- a + \frac{3 \pi}{2}\right)} + e^{i \left(a - \frac{3 \pi}{2}\right)}\right)}{2}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(- \frac{i \left(e^{i a} - e^{- i a}\right)}{2} + \frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right) \cot{\left(a \right)}}$$
/ pi \
(-cos(a) - sin(a))*cot|-----|
\2 - a/
-----------------------------
(cos(a) + sin(a))*cot(a)
$$\frac{\left(- \sin{\left(a \right)} - \cos{\left(a \right)}\right) \cot{\left(\frac{\pi}{2 - a} \right)}}{\left(\sin{\left(a \right)} + \cos{\left(a \right)}\right) \cot{\left(a \right)}}$$
/ pi \
-cot|-----|
\2 - a/
------------
cot(a)
$$- \frac{\cot{\left(\frac{\pi}{2 - a} \right)}}{\cot{\left(a \right)}}$$
-cot(pi/(2 - a))/cot(a)