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