Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(pi/2+a)*(-cot(a-3*pi/2))/(-sin(a))^2-tan(a-3*pi/2)*(-cos(a))
¿Cómo vas a descomponer esta sin(pi/2+a)*(-cot(a-3*pi/2))/(-sin(a))^2-tan(a-3*pi/2)*(-cos(a)) expresión en fracciones?
Solución
Ha introducido
[src]
/pi \ / / 3*pi\\
sin|-- + a|*|-cot|a - ----||
\2 / \ \ 2 // / 3*pi\
---------------------------- - tan|a - ----|*(-cos(a))
2 \ 2 /
(-sin(a))
$$- - \cos{\left(a \right)} \tan{\left(a - \frac{3 \pi}{2} \right)} + \frac{\sin{\left(a + \frac{\pi}{2} \right)} \left(- \cot{\left(a - \frac{3 \pi}{2} \right)}\right)}{\left(- \sin{\left(a \right)}\right)^{2}}$$
(sin(pi/2 + a)*(-cot(a - 3*pi/2)))/(-sin(a))^2 - tan(a - 3*pi/2)*(-cos(a))
Denominador racional
[src]
/ pi\ 2
sin|a + --|*tan(a) - sin (a)*cos(a)*cot(a)
\ 2 /
------------------------------------------
2
sin (a)
$$\frac{- \sin^{2}{\left(a \right)} \cos{\left(a \right)} \cot{\left(a \right)} + \sin{\left(a + \frac{\pi}{2} \right)} \tan{\left(a \right)}}{\sin^{2}{\left(a \right)}}$$
(sin(a + pi/2)*tan(a) - sin(a)^2*cos(a)*cot(a))/sin(a)^2
Denominador común
[src]
cos(a)*tan(a)
-cos(a)*cot(a) + -------------
2
sin (a)
$$- \cos{\left(a \right)} \cot{\left(a \right)} + \frac{\cos{\left(a \right)} \tan{\left(a \right)}}{\sin^{2}{\left(a \right)}}$$
-cos(a)*cot(a) + cos(a)*tan(a)/sin(a)^2
Potencias
[src]
/ / 3*pi\ / 3*pi\\
| I*|a - ----| I*|-a + ----|| / I*a -I*a\ / / pi\ / pi\\
| \ 2 / \ 2 /| | e e | | I*|-a - --| I*|a + --||
I*\- e + e /*|- ---- - -----| | \ 2 / \ 2 /|
\ 2 2 / 2*I*\- e + e /*tan(a)
- ----------------------------------------------------- + -----------------------------------------
/ 3*pi\ / 3*pi\ 2
I*|a - ----| I*|-a + ----| / -I*a I*a\
\ 2 / \ 2 / \- e + e /
e + e
$$- \frac{i \left(- \frac{e^{i a}}{2} - \frac{e^{- i a}}{2}\right) \left(e^{i \left(- a + \frac{3 \pi}{2}\right)} - e^{i \left(a - \frac{3 \pi}{2}\right)}\right)}{e^{i \left(- a + \frac{3 \pi}{2}\right)} + e^{i \left(a - \frac{3 \pi}{2}\right)}} + \frac{2 i \left(- e^{i \left(- a - \frac{\pi}{2}\right)} + e^{i \left(a + \frac{\pi}{2}\right)}\right) \tan{\left(a \right)}}{\left(e^{i a} - e^{- i a}\right)^{2}}$$
cos(a)*tan(a)
-cos(a)*cot(a) + -------------
2
sin (a)
$$- \cos{\left(a \right)} \cot{\left(a \right)} + \frac{\cos{\left(a \right)} \tan{\left(a \right)}}{\sin^{2}{\left(a \right)}}$$
-cos(a)*cot(a) + cos(a)*tan(a)/sin(a)^2
Unión de expresiones racionales
[src]
/-3*pi + 2*a\ /pi + 2*a\ 2 /-3*pi + 2*a\
- cot|-----------|*sin|--------| + sin (a)*cos(a)*tan|-----------|
\ 2 / \ 2 / \ 2 /
------------------------------------------------------------------
2
sin (a)
$$\frac{\sin^{2}{\left(a \right)} \cos{\left(a \right)} \tan{\left(\frac{2 a - 3 \pi}{2} \right)} - \sin{\left(\frac{2 a + \pi}{2} \right)} \cot{\left(\frac{2 a - 3 \pi}{2} \right)}}{\sin^{2}{\left(a \right)}}$$
(-cot((-3*pi + 2*a)/2)*sin((pi + 2*a)/2) + sin(a)^2*cos(a)*tan((-3*pi + 2*a)/2))/sin(a)^2
Combinatoria
[src]
/ 2 \
-\-tan(a) + sin (a)*cot(a)/*cos(a)
-----------------------------------
2
sin (a)
$$- \frac{\left(\sin^{2}{\left(a \right)} \cot{\left(a \right)} - \tan{\left(a \right)}\right) \cos{\left(a \right)}}{\sin^{2}{\left(a \right)}}$$
-(-tan(a) + sin(a)^2*cot(a))*cos(a)/sin(a)^2
Compilar la expresión
[src]
/ 3*pi\ /pi \
cot|a - ----|*sin|-- + a|
/ 3*pi\ \ 2 / \2 /
cos(a)*tan|a - ----| - -------------------------
\ 2 / 2
sin (a)
$$\cos{\left(a \right)} \tan{\left(a - \frac{3 \pi}{2} \right)} - \frac{\sin{\left(a + \frac{\pi}{2} \right)} \cot{\left(a - \frac{3 \pi}{2} \right)}}{\sin^{2}{\left(a \right)}}$$
cos(a)*tan(a - 3*pi/2) - cot(a - 3*pi/2)*sin(pi/2 + a)/sin(a)^2
Parte trigonométrica
[src]
sin(a)
$$\sin{\left(a \right)}$$
2
/ 2/a\\ / 2/a\\ /a pi\
|1 - tan |-||*cot(a) |1 + tan |-|| *tan|- + --|
\ \2// \ \2// \2 4 /
- -------------------- + -----------------------------------
2/a\ / 2/a pi\\ 2/a\
1 + tan |-| 2*|1 + tan |- + --||*cot(a)*tan |-|
\2/ \ \2 4 // \2/
$$- \frac{\left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \cot{\left(a \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{2 \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}$$
/ pi\
sec|a - --|
\ 2 / / pi\
- ----------- + sec|a - --|
2 \ 2 /
sec (a)
$$\sec{\left(a - \frac{\pi}{2} \right)} - \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}}$$
/ 1 \
|1 - ---------|*tan(a)
2/a\ | 2/a\|
1 - 2*sin |-| | 2*cos |-||
\2/ \ \2//
- ------------- + ----------------------
tan(a) 2/a\
2*sin |-|
\2/
$$- \frac{1 - 2 \sin^{2}{\left(\frac{a}{2} \right)}}{\tan{\left(a \right)}} + \frac{\left(1 - \frac{1}{2 \cos^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(a \right)}}{2 \sin^{2}{\left(\frac{a}{2} \right)}}$$
/ 2/a pi\\ / / pi\\ / pi\ /a pi\
|1 - 2*cos |- - --||*cos(a) |1 + cos|a - --||*cos|a - --|*cos|- + --|
\ \2 2 // \ \ 2 // \ 2 / \2 4 /
- --------------------------- + -----------------------------------------
/ pi\ 2/a\ 2/a pi\ /a pi\
cos|a - --| 4*cos(a)*cos |-|*cos |- - --|*cos|- - --|
\ 2 / \2/ \2 2 / \2 4 /
$$- \frac{\left(1 - 2 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}\right) \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + \frac{\left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{a}{2} + \frac{\pi}{4} \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{4 \cos^{2}{\left(\frac{a}{2} \right)} \cos{\left(a \right)} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}$$
/ 2 \ / 2/pi a\\
|1 - -------|*csc(a) | csc |-- - -||
| 2/a\| 2/a\ | \2 2/| /pi \
| csc |-|| csc |-|*|1 - ------------|*csc|-- - a|
\ \2// \2/ \ 2 / \2 /
- -------------------- + --------------------------------------
/pi \ 2*csc(a)
csc|-- - a|
\2 /
$$- \frac{\left(1 - \frac{2}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{2}\right) \csc^{2}{\left(\frac{a}{2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}{2 \csc{\left(a \right)}}$$
1 / 3*pi\ ------ + cos(a)*tan|a - ----| sin(a) \ 2 /
$$\cos{\left(a \right)} \tan{\left(a - \frac{3 \pi}{2} \right)} + \frac{1}{\sin{\left(a \right)}}$$
/ /a\ \
4 | 2*cot|-| |
/ 2/a\\ | \2/ | /a pi\
|1 + cot |-|| *|1 + -----------|*cot|- + --|
/ 2/a\ \ \ \4// | 2/a\| \2 4 /
| 8*cot |-| | | 1 + cot |-||
| \4/ | \ \2//
- |1 - --------------|*cot(a) + --------------------------------------------
| 2| 2/a\ 4/a\
| / 2/a\\ | 64*cot(a)*cot |-|*cot |-|
| |1 + cot |-|| | \2/ \4/
\ \ \4// /
$$- \left(1 - \frac{8 \cot^{2}{\left(\frac{a}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}\right) \cot{\left(a \right)} + \frac{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{64 \cot^{4}{\left(\frac{a}{4} \right)} \cot^{2}{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}$$
2/a\ 4/a\ /a pi\
tan |-|*tan |-|*(1 + sin(a))*cot|- + --|*tan(a)
\2/ \4/ \2 4 /
-cos(a)*cot(a) + -----------------------------------------------
8/a\
64*sin |-|
\4/
$$\frac{\left(\sin{\left(a \right)} + 1\right) \tan^{4}{\left(\frac{a}{4} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{64 \sin^{8}{\left(\frac{a}{4} \right)}} - \cos{\left(a \right)} \cot{\left(a \right)}$$
/pi \
csc(a)*csc|-- - a|
csc(a) \2 /
- ------------ + ------------------
2/pi \ sec(a)
csc |-- - a|
\2 /
$$\frac{\csc{\left(a \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} - \frac{\csc{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}$$
2/a\
8*tan |-| / /a\ \
\4/ 4 | 2*tan|-| |
1 - -------------- / 2/a\\ 2/a\ | \2/ |
2 |1 + tan |-|| *tan |-|*|1 + -----------|*tan(a)
/ 2/a\\ \ \4// \2/ | 2/a\|
|1 + tan |-|| | 1 + tan |-||
\ \4// \ \2//
- ------------------ + -----------------------------------------------
tan(a) 4/a\ /a pi\
64*tan |-|*tan|- + --|
\4/ \2 4 /
$$- \frac{1 - \frac{8 \tan^{2}{\left(\frac{a}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}}{\tan{\left(a \right)}} + \frac{\left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)}}{64 \tan^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$
cos(a)*cos(a - 2*pi) cos(a)*sin(a)
- -------------------- + --------------------------
sin(a) 2/ pi\
cos(a - 2*pi)*cos |a - --|
\ 2 /
$$\frac{\sin{\left(a \right)} \cos{\left(a \right)}}{\cos{\left(a - 2 \pi \right)} \cos^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{\cos{\left(a \right)} \cos{\left(a - 2 \pi \right)}}{\sin{\left(a \right)}}$$
2 / 1 \
sin (a)*|1 - --------------|
/ 2/a\\ | 2/pi a\|
|1 - 2*sin |-||*sin(2*a) | 2*sin |-- + -||
\ \2// \ \2 2//
- ------------------------ + ----------------------------
2 2/a\
2*sin (a) sin |-|*sin(2*a)
\2/
$$- \frac{\left(1 - 2 \sin^{2}{\left(\frac{a}{2} \right)}\right) \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}} + \frac{\left(1 - \frac{1}{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}}\right) \sin^{2}{\left(a \right)}}{\sin^{2}{\left(\frac{a}{2} \right)} \sin{\left(2 a \right)}}$$
/ pi\
cos|a - --| 2
\ 2 / cos (a)
----------- - -----------
2 / pi\
sin (a) cos|a - --|
\ 2 /
$$- \frac{\cos^{2}{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}} + \frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\sin^{2}{\left(a \right)}}$$
2
2/a\ / 2/a\\ /a pi\
-1 + cot |-| |1 + cot |-|| *cot|- + --|*tan(a)
\2/ \ \2// \2 4 /
- -------------------- + ---------------------------------
/ 2/a\\ / 2/a pi\\ 2/a\
|1 + cot |-||*tan(a) 2*|1 + cot |- + --||*cot |-|
\ \2// \ \2 4 // \2/
$$- \frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(a \right)}} + \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \cot^{2}{\left(\frac{a}{2} \right)}}$$
/a\
2*cot|-|
\2/
-----------
2/a\
1 + cot |-|
\2/
$$\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}$$
2/ pi\
2*sin |a + --|*cos(a)
sin(2*a) \ 2 /
--------------------- - ---------------------
2 / pi\ sin(2*a)
2*sin (a)*sin|a + --|
\ 2 /
$$- \frac{2 \sin^{2}{\left(a + \frac{\pi}{2} \right)} \cos{\left(a \right)}}{\sin{\left(2 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)} \sin{\left(a + \frac{\pi}{2} \right)}}$$
/ 1 \ / pi\
|1 - ---------|*cos|a - --|
/ 2/a pi\\ | 2/a\| \ 2 /
|1 - 2*cos |- - --||*cos(a) | 2*cos |-||
\ \2 2 // \ \2//
- --------------------------- + ---------------------------
/ pi\ 2/a pi\
cos|a - --| 2*cos(a)*cos |- - --|
\ 2 / \2 2 /
$$\frac{\left(1 - \frac{1}{2 \cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos{\left(a - \frac{\pi}{2} \right)}}{2 \cos{\left(a \right)} \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - \frac{\left(1 - 2 \cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}\right) \cos{\left(a \right)}}{\cos{\left(a - \frac{\pi}{2} \right)}}$$
2 / pi\
2*cos (a)*sin|a + --|
sin(2*a) \ 2 /
---------------- - ---------------------
2 sin(2*a)
2*cos(a)*sin (a)
$$- \frac{2 \sin{\left(a + \frac{\pi}{2} \right)} \cos^{2}{\left(a \right)}}{\sin{\left(2 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)} \cos{\left(a \right)}}$$
csc(a)
- ------- + csc(a)
2
sec (a)
$$\csc{\left(a \right)} - \frac{\csc{\left(a \right)}}{\sec^{2}{\left(a \right)}}$$
1 ------ csc(a)
$$\frac{1}{\csc{\left(a \right)}}$$
/ 2 \
/ /a\\ |sin (a) |
2*|1 - tan|-||*|------- + tan(a)|
2 \ \2// \ cos(a) /
- cos (a)*csc(a) + ---------------------------------
/ /a\\
(1 - cos(2*a))*|1 + tan|-||
\ \2//
$$- \cos^{2}{\left(a \right)} \csc{\left(a \right)} + \frac{2 \left(1 - \tan{\left(\frac{a}{2} \right)}\right) \left(\frac{\sin^{2}{\left(a \right)}}{\cos{\left(a \right)}} + \tan{\left(a \right)}\right)}{\left(1 - \cos{\left(2 a \right)}\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)}$$
2
2/a\ / 2/a\\ /a pi\
1 - tan |-| |1 + tan |-|| *tan(a)*tan|- + --|
\2/ \ \2// \2 4 /
- -------------------- + ---------------------------------
/ 2/a\\ / 2/a pi\\ 2/a\
|1 + tan |-||*tan(a) 2*|1 + tan |- + --||*tan |-|
\ \2// \ \2 4 // \2/
$$- \frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(a \right)}} + \frac{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{2 \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)}}$$
2
/ 2/a\\ / 2/a\\ /a pi\
|-1 + cot |-||*cot(a) |1 + cot |-|| *cot|- + --|
\ \2// \ \2// \2 4 /
- --------------------- + -----------------------------------
2/a\ / 2/a pi\\ 2/a\
1 + cot |-| 2*|1 + cot |- + --||*cot(a)*cot |-|
\2/ \ \2 4 // \2/
$$- \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \cot{\left(a \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} + \frac{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \cot^{2}{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}$$
/ 2 \ / pi\ 2/a\ 2/a pi\ / 1 \ /a pi\
|1 - ------------|*sec|a - --| sec |-|*sec |- - --|*|1 + -----------|*sec(a)*sec|- - --|
| 2/a pi\| \ 2 / \2/ \2 2 / | / pi\| \2 4 /
| sec |- - --|| | sec|a - --||
\ \2 2 // \ \ 2 //
- ------------------------------ + ---------------------------------------------------------
sec(a) / pi\ /a pi\
4*sec|a - --|*sec|- + --|
\ 2 / \2 4 /
$$- \frac{\left(1 - \frac{2}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}\right) \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}} + \frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \sec^{2}{\left(\frac{a}{2} \right)} \sec{\left(a \right)} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{4 \sec{\left(\frac{a}{2} + \frac{\pi}{4} \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
/a\
2*tan|-|
\2/
-----------
2/a\
1 + tan |-|
\2/
$$\frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}$$
/ 2 \
| / 2/a\\ |
2 | |1 + cot |-|| |
/ 2/a\\ | \ \4// |
|1 + cot |-|| *|1 - -----------------|
\ \4// | 2|
/ 2/a\ \ | / 2/a\\ |
| 8*cot |-| | | 2*|-1 + cot |-|| |
| \4/ | \ \ \4// /
- |1 - --------------|*cot(a) + --------------------------------------
| 2| 2/a\
| / 2/a\\ | 8*cot(a)*cot |-|
| |1 + cot |-|| | \4/
\ \ \4// /
$$\frac{\left(1 - \frac{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}{2 \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}{8 \cot^{2}{\left(\frac{a}{4} \right)} \cot{\left(a \right)}} - \left(1 - \frac{8 \cot^{2}{\left(\frac{a}{4} \right)}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}\right) \cot{\left(a \right)}$$
/ 2 \
/ /a\\ |sin (a) |
2 2*|1 - tan|-||*|------- + tan(a)|
cos (a) \ \2// \ cos(a) /
- ------- - ---------------------------------
sin(a) / /a\\
|1 + tan|-||*(-1 + cos(2*a))
\ \2//
$$- \frac{2 \left(1 - \tan{\left(\frac{a}{2} \right)}\right) \left(\frac{\sin^{2}{\left(a \right)}}{\cos{\left(a \right)}} + \tan{\left(a \right)}\right)}{\left(\cos{\left(2 a \right)} - 1\right) \left(\tan{\left(\frac{a}{2} \right)} + 1\right)} - \frac{\cos^{2}{\left(a \right)}}{\sin{\left(a \right)}}$$
1 ----------- / pi\ sec|a - --| \ 2 /
$$\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}$$
/ 2 \
2/a\ | / 2/a\\ |
8*tan |-| 2 | |1 + tan |-|| |
\4/ / 2/a\\ | \ \4// |
1 - -------------- |1 + tan |-|| *|1 - ----------------|*tan(a)
2 \ \4// | 2|
/ 2/a\\ | / 2/a\\ |
|1 + tan |-|| | 2*|1 - tan |-|| |
\ \4// \ \ \4// /
- ------------------ + --------------------------------------------
tan(a) 2/a\
8*tan |-|
\4/
$$\frac{\left(1 - \frac{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}{2 \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2}}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan{\left(a \right)}}{8 \tan^{2}{\left(\frac{a}{4} \right)}} - \frac{1 - \frac{8 \tan^{2}{\left(\frac{a}{4} \right)}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2}}}{\tan{\left(a \right)}}$$
/ 2 \
|1 - -------|*csc(a)
| 2/a\| 2/a\ 2/pi a\ / 1 \ /pi \ /a pi\
| csc |-|| csc |-|*csc |-- - -|*|1 + ------|*csc|-- - a|*csc|- + --|
\ \2// \2/ \2 2/ \ csc(a)/ \2 / \2 4 /
- -------------------- + ---------------------------------------------------------
/pi \ / a pi\
csc|-- - a| 4*csc(a)*csc|- - + --|
\2 / \ 2 4 /
$$- \frac{\left(1 - \frac{2}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\left(1 + \frac{1}{\csc{\left(a \right)}}\right) \csc^{2}{\left(\frac{a}{2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)} \csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)} \csc{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{4 \csc{\left(a \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}$$
/ pi\ cos|a - --| \ 2 /
$$\cos{\left(a - \frac{\pi}{2} \right)}$$
2/a\ 2/a\ /a pi\
1 - 2*sin |-| tan |-|*(1 + sin(a))*cot|- + --|*tan(a)
\2/ \2/ \2 4 /
- ------------- + ---------------------------------------
tan(a) 4/a\
4*sin |-|
\2/
$$- \frac{1 - 2 \sin^{2}{\left(\frac{a}{2} \right)}}{\tan{\left(a \right)}} + \frac{\left(\sin{\left(a \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)} \cot{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}$$
csc(a) csc(a)*sec(a)
- ------- + -------------
2 /pi \
sec (a) csc|-- - a|
\2 /
$$- \frac{\csc{\left(a \right)}}{\sec^{2}{\left(a \right)}} + \frac{\csc{\left(a \right)} \sec{\left(a \right)}}{\csc{\left(- a + \frac{\pi}{2} \right)}}$$
/ 2 \ / pi\ / 2/a\\
|1 - ------------|*sec|a - --| | sec |-||
| 2/a pi\| \ 2 / 2/a pi\ | \2/|
| sec |- - --|| sec |- - --|*|1 - -------|*sec(a)
\ \2 2 // \2 2 / \ 2 /
- ------------------------------ + ---------------------------------
sec(a) / pi\
2*sec|a - --|
\ 2 /
$$\frac{\left(1 - \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{2}\right) \sec{\left(a \right)} \sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{2 \sec{\left(a - \frac{\pi}{2} \right)}} - \frac{\left(1 - \frac{2}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}\right) \sec{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(a \right)}}$$
/ 1 \ / /a\\
2 |1 + ------|*|1 - tan|-||
cos (a) \ sin(a)/ \ \2//
- ------- + -------------------------
sin(a) / /a\\
|1 + tan|-||*cos(a)
\ \2//
$$\frac{\left(1 + \frac{1}{\sin{\left(a \right)}}\right) \left(1 - \tan{\left(\frac{a}{2} \right)}\right)}{\left(\tan{\left(\frac{a}{2} \right)} + 1\right) \cos{\left(a \right)}} - \frac{\cos^{2}{\left(a \right)}}{\sin{\left(a \right)}}$$
2/a\
tan |-|*(1 + sin(a))*tan(a)
cos(a) \2/
- ------ + ------------------------------
tan(a) 8/a\ 4/a\ /a pi\
64*cos |-|*tan |-|*tan|- + --|
\4/ \4/ \2 4 /
$$\frac{\left(\sin{\left(a \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)} \tan{\left(a \right)}}{64 \cos^{8}{\left(\frac{a}{4} \right)} \tan^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - \frac{\cos{\left(a \right)}}{\tan{\left(a \right)}}$$
/ 2/a\\
|1 - 2*sin |-||*sin(2*a)
\ \2// (1 + sin(a))*cos(a)
- ------------------------ + ---------------------
2 2/a pi\
2*sin (a) sin(2*a)*sin |- + --|
\2 4 /
$$- \frac{\left(1 - 2 \sin^{2}{\left(\frac{a}{2} \right)}\right) \sin{\left(2 a \right)}}{2 \sin^{2}{\left(a \right)}} + \frac{\left(\sin{\left(a \right)} + 1\right) \cos{\left(a \right)}}{\sin{\left(2 a \right)} \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}$$
-(1 - 2*sin(a/2)^2)*sin(2*a)/(2*sin(a)^2) + (1 + sin(a))*cos(a)/(sin(2*a)*sin(a/2 + pi/4)^2)
Respuesta numérica
[src]
cos(a)*tan(a - 3*pi/2) - cot(a - 3*pi/2)*sin(pi/2 + a)/sin(a)^2
cos(a)*tan(a - 3*pi/2) - cot(a - 3*pi/2)*sin(pi/2 + a)/sin(a)^2