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|-- + a|*sin(pi - a)
2 \2 /
sin (a) - -------------------------
/3*pi \
tan(pi - a)*cot|---- + a|
\ 2 /
$$- \frac{\sin{\left(\pi - a \right)} \cos{\left(a + \frac{\pi}{2} \right)}}{\tan{\left(\pi - a \right)} \cot{\left(a + \frac{3 \pi}{2} \right)}} + \sin^{2}{\left(a \right)}$$
sin(a)^2 - cos(pi/2 + a)*sin(pi - a)/(tan(pi - a)*cot((3*pi)/2 + a))
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))
Denominador racional
[src]
2 2 / pi\
sin (a)*tan (a) - cos|a + --|*sin(a)
\ 2 /
------------------------------------
2
tan (a)
$$\frac{\sin^{2}{\left(a \right)} \tan^{2}{\left(a \right)} - \sin{\left(a \right)} \cos{\left(a + \frac{\pi}{2} \right)}}{\tan^{2}{\left(a \right)}}$$
(sin(a)^2*tan(a)^2 - cos(a + pi/2)*sin(a))/tan(a)^2
Unión de expresiones racionales
[src]
/ /2*a + 3*pi\ /pi + 2*a\\
|cot|----------|*sin(a)*tan(a) + cos|--------||*sin(a)
\ \ 2 / \ 2 //
------------------------------------------------------
/2*a + 3*pi\
cot|----------|*tan(a)
\ 2 /
$$\frac{\left(\sin{\left(a \right)} \tan{\left(a \right)} \cot{\left(\frac{2 a + 3 \pi}{2} \right)} + \cos{\left(\frac{2 a + \pi}{2} \right)}\right) \sin{\left(a \right)}}{\tan{\left(a \right)} \cot{\left(\frac{2 a + 3 \pi}{2} \right)}}$$
(cot((2*a + 3*pi)/2)*sin(a)*tan(a) + cos((pi + 2*a)/2))*sin(a)/(cot((2*a + 3*pi)/2)*tan(a))
Combinatoria
[src]
2 / 2 \
sin (a)*\1 + tan (a)/
---------------------
2
tan (a)
$$\frac{\left(\tan^{2}{\left(a \right)} + 1\right) \sin^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)}}$$
sin(a)^2*(1 + tan(a)^2)/tan(a)^2
Potencias
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/ / pi\ / pi\\
| I*|a + --| I*|-a - --||
| \ 2 / \ 2 /|
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)
$$- \frac{\left(e^{i a} - e^{- i a}\right)^{2}}{4} - \frac{\left(e^{i \left(\pi - a\right)} - e^{i \left(a - \pi\right)}\right) \left(e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right) \left(\frac{e^{i \left(- a - \frac{\pi}{2}\right)}}{2} + \frac{e^{i \left(a + \frac{\pi}{2}\right)}}{2}\right)}{2 \left(- e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right) \tan{\left(a \right)}}$$
2
2 sin (a)
sin (a) + -------
2
tan (a)
$$\sin^{2}{\left(a \right)} + \frac{\sin^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)}}$$
sin(a)^2 + sin(a)^2/tan(a)^2
Compilar la expresión
[src]
/pi \
cos|-- + a|*sin(pi - a)
2 \2 /
sin (a) - -------------------------
/3*pi \
cot|---- + a|*tan(pi - a)
\ 2 /
$$\sin^{2}{\left(a \right)} - \frac{\sin{\left(\pi - a \right)} \cos{\left(a + \frac{\pi}{2} \right)}}{\tan{\left(\pi - a \right)} \cot{\left(a + \frac{3 \pi}{2} \right)}}$$
sin(a)^2 - cos(pi/2 + a)*sin(pi - a)/(cot((3*pi)/2 + a)*tan(pi - a))
Parte trigonométrica
[src]
/pi \ 2 / / pi\\
sin|-- + 2*a| sin (2*a)*|-1 + sin|a + --||
1 \2 / \ \ 2 //
- - ------------- - ----------------------------
2 2 / 4/a\\
| 4*sin |-||
| \2/| 4
2*|1 + ---------|*sin (a)
| 2 |
\ sin (a) /
$$- \frac{\sin{\left(2 a + \frac{\pi}{2} \right)}}{2} + \frac{1}{2} - \frac{\left(\sin{\left(a + \frac{\pi}{2} \right)} - 1\right) \sin^{2}{\left(2 a \right)}}{2 \left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \sin^{4}{\left(a \right)}}$$
2/ pi\
sec |a - --|
1 \ 2 /
------------ + --------------------------
2/ pi\ 2 /pi \
sec |a - --| csc(a)*sec (a)*sec|-- - a|
\ 2 / \2 /
$$\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + \frac{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\csc{\left(a \right)} \sec^{2}{\left(a \right)} \sec{\left(- a + \frac{\pi}{2} \right)}}$$
2/a\ / 2/a pi\\ /a\
cos |-|*(1 + sin(a))*|-1 + cot |- + --||*cot(a)*tan|-|
1 - cos(2*a) \2/ \ \2 4 // \2/
------------ - ------------------------------------------------------
2 tan(a)
$$\frac{1 - \cos{\left(2 a \right)}}{2} - \frac{\left(\sin{\left(a \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \cos^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}{\tan{\left(a \right)}}$$
2
1 cos(2*a) 2*cos (a)*(-1 + cos(a))
- - -------- - -----------------------
2 2 2 4/a\
sin (a) + 4*sin |-|
\2/
$$- \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2} - \frac{2 \left(\cos{\left(a \right)} - 1\right) \cos^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}}$$
/ /a\ \
2 | 2*cot|-| |
/ 2/a\\ 2 | \2/ | / 2/a pi\\
|-1 + cot |-|| *cot (a)*|1 + -----------|*|-1 + cot |- + --||
\ \4// | 2/a\| \ \2 4 //
2 | 1 + cot |-||
1 -1 + cot (a) \ \2//
- - --------------- - -------------------------------------------------------------
2 / 2 \ 2
2*\1 + cot (a)/ / 2/a\\ /a\
|1 + cot |-|| *cot|-|
\ \4// \2/
$$- \frac{\left(1 + \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \cot^{2}{\left(a \right)}}{\left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \cot{\left(\frac{a}{2} \right)}} - \frac{\cot^{2}{\left(a \right)} - 1}{2 \left(\cot^{2}{\left(a \right)} + 1\right)} + \frac{1}{2}$$
1 csc(a)
------- + -------------------
2 2 /pi \
csc (a) sec (a)*sec|-- - a|
\2 /
$$\frac{\csc{\left(a \right)}}{\sec^{2}{\left(a \right)} \sec{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$
1 - cos(2*a) 2*(-1 + cos(a))
------------ - ---------------------
2 / 2/a\\ 2
|1 + tan |-||*tan (a)
\ \2//
$$\frac{1 - \cos{\left(2 a \right)}}{2} - \frac{2 \left(\cos{\left(a \right)} - 1\right)}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan^{2}{\left(a \right)}}$$
2/a\ / 2/a pi\\ /a\
4*cot |-| 2*|-1 + cot |- + --||*cot(a)*tan|-|
\2/ \ \2 4 // \2/
-------------- - ---------------------------------------
2 / 2/a pi\\ / 2/a\\
/ 2/a\\ |1 + cot |- + --||*|1 + tan |-||*tan(a)
|1 + cot |-|| \ \2 4 // \ \2//
\ \2//
$$\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - \frac{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \tan{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(a \right)}}$$
2 2/ pi\
sin (a) + sin |a + --|
\ 2 /
$$\sin^{2}{\left(a \right)} + \sin^{2}{\left(a + \frac{\pi}{2} \right)}$$
1 1
------- + ------------
2 2/pi \
csc (a) csc |-- - a|
\2 /
$$\frac{1}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$
2 / 1 \
2*csc (a)*|-1 + -----------|
| /pi \|
| csc|-- - a||
1 1 \ \2 //
- - --------------- - -------------------------------
2 /pi \ / 2/pi a\\
2*csc|-- - 2*a| | csc |-- - -||
\2 / | \2 2/| 2/pi \
|1 + ------------|*csc |-- - a|
| 2/a\ | \2 /
| csc |-| |
\ \2/ /
$$- \frac{2 \left(-1 + \frac{1}{\csc{\left(- a + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(a \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc^{2}{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{2} - \frac{1}{2 \csc{\left(- 2 a + \frac{\pi}{2} \right)}}$$
1 1 ------- + ------- 2 2 csc (a) sec (a)
$$\frac{1}{\sec^{2}{\left(a \right)}} + \frac{1}{\csc^{2}{\left(a \right)}}$$
/ 2/a\\
| -1 + cot |-||
2 | \2/|
2*cot (a)*|-1 + ------------|
| 2/a\ |
2 | 1 + cot |-| |
1 -1 + cot (a) \ \2/ /
- - --------------- - -----------------------------
2 / 2 \ 1
2*\1 + cot (a)/ 1 + -------
2/a\
cot |-|
\2/
$$- \frac{\cot^{2}{\left(a \right)} - 1}{2 \left(\cot^{2}{\left(a \right)} + 1\right)} + \frac{1}{2} - \frac{2 \left(\frac{\cot^{2}{\left(\frac{a}{2} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} - 1\right) \cot^{2}{\left(a \right)}}{1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}}$$
/ 2/a pi\ \
| csc |- + --| |
2 / 1 \ | \2 4 / |
csc (a)*|1 + ------|*|-1 + --------------|
\ csc(a)/ | 2/ a pi\|
| csc |- - + --||
1 1 \ \ 2 4 //
- - --------------- - ------------------------------------------
2 /pi \ /a\ 2/pi \ /pi a\
2*csc|-- - 2*a| csc|-|*csc |-- - a|*csc|-- - -|
\2 / \2/ \2 / \2 2/
$$- \frac{\left(-1 + \frac{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{1}{\csc{\left(a \right)}}\right) \csc^{2}{\left(a \right)}}{\csc{\left(\frac{a}{2} \right)} \csc^{2}{\left(- a + \frac{\pi}{2} \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + \frac{1}{2} - \frac{1}{2 \csc{\left(- 2 a + \frac{\pi}{2} \right)}}$$
2/ pi\ / 1 \
2*sec |a - --|*|-1 + ------|
1 1 \ 2 / \ sec(a)/
- - ---------- - ----------------------------
2 2*sec(2*a) / 2/a\ \
| sec |-| |
| \2/ | 2
|1 + ------------|*sec (a)
| 2/a pi\|
| sec |- - --||
\ \2 2 //
$$- \frac{2 \left(-1 + \frac{1}{\sec{\left(a \right)}}\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec^{2}{\left(a \right)}} + \frac{1}{2} - \frac{1}{2 \sec{\left(2 a \right)}}$$
2/ pi\
cos |a - --| - cos(a)*cos(pi + a)
\ 2 /
$$- \cos{\left(a \right)} \cos{\left(a + \pi \right)} + \cos^{2}{\left(a - \frac{\pi}{2} \right)}$$
2/a\ 2 / 2/a pi\\
4*cot |-| 2*cot (a)*|-1 + cot |- + --||
\2/ \ \2 4 //
-------------- - ---------------------------------------
2 / 1 \ / 2/a pi\\ /a\
/ 2/a\\ |1 + -------|*|1 + cot |- + --||*cot|-|
|1 + cot |-|| | 2/a\| \ \2 4 // \2/
\ \2// | cot |-||
\ \2//
$$\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - \frac{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \cot^{2}{\left(a \right)}}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \cot{\left(\frac{a}{2} \right)}}$$
2/a\ / 2/a pi\\
4*tan |-| 2*|1 - tan |- + --||
\2/ \ \2 4 //
-------------- - -----------------------------------------------
2 / 1 \ / 2/a pi\\ 2 /a\
/ 2/a\\ |1 + -------|*|1 + tan |- + --||*tan (a)*tan|-|
|1 + tan |-|| | 2/a\| \ \2 4 // \2/
\ \2// | tan |-||
\ \2//
$$\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} - \frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right)}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(a \right)}}$$
2 1 cos(2*a) / 2/a\\ 2 4/a\ / 2/a pi\\ /a\ - - -------- - |-1 + cot |-|| *cot (a)*sin |-|*(1 + sin(a))*|-1 + cot |- + --||*tan|-| 2 2 \ \4// \4/ \ \2 4 // \2/
$$- \left(\sin{\left(a \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \sin^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} \right)} \cot^{2}{\left(a \right)} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2}$$
2
2 cos (a)*sin(pi + a)
sin (a) - -------------------
sin(a)
$$\sin^{2}{\left(a \right)} - \frac{\sin{\left(a + \pi \right)} \cos^{2}{\left(a \right)}}{\sin{\left(a \right)}}$$
1
$$1$$
2 2 cos (a) + sin (a)
$$\sin^{2}{\left(a \right)} + \cos^{2}{\left(a \right)}$$
2
/ 2/a\\ 4/a\ / 1 \ /a\
|1 - tan |-|| *cos |-|*(1 + sin(a))*|-1 + ------------|*tan|-|
\ \4// \4/ | 2/a pi\| \2/
| tan |- + --||
1 cos(2*a) \ \2 4 //
- - -------- - --------------------------------------------------------------
2 2 2
tan (a)
$$- \frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2} \left(\sin{\left(a \right)} + 1\right) \cos^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(a \right)}} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2}$$
/ 2/a pi\\
| sec |- - --||
2/ pi\ / 1 \ | \2 4 /|
sec |a - --|*|1 + -----------|*|-1 + ------------|
\ 2 / | / pi\| | 2/a pi\|
| sec|a - --|| | sec |- + --||
1 1 \ \ 2 // \ \2 4 //
- - ---------- - --------------------------------------------------
2 2*sec(2*a) 2 /a\ /a pi\
sec (a)*sec|-|*sec|- - --|
\2/ \2 2 /
$$- \frac{\left(1 + \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}\right) \left(\frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}} - 1\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec{\left(\frac{a}{2} \right)} \sec^{2}{\left(a \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + \frac{1}{2} - \frac{1}{2 \sec{\left(2 a \right)}}$$
/ /a\ \
2 | 2*tan|-| |
/ 2/a\\ | \2/ | / 1 \ /a\
|1 - tan |-|| *|1 + -----------|*|-1 + ------------|*tan|-|
\ \4// | 2/a\| | 2/a pi\| \2/
2 | 1 + tan |-|| | tan |- + --||
1 1 - tan (a) \ \2// \ \2 4 //
- - --------------- - -----------------------------------------------------------
2 / 2 \ 2
2*\1 + tan (a)/ / 2/a\\ 2
|1 + tan |-|| *tan (a)
\ \4//
$$- \frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(1 + \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}\right) \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{2} \tan{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{2} \tan^{2}{\left(a \right)}} - \frac{1 - \tan^{2}{\left(a \right)}}{2 \left(\tan^{2}{\left(a \right)} + 1\right)} + \frac{1}{2}$$
2/a\ / 2/a pi\\ /a\
4*tan |-| 2*|1 - tan |- + --||*cot(a)*cot|-|
\2/ \ \2 4 // \2/
-------------- - ---------------------------------------
2 / 2/a\\ / 2/a pi\\
/ 2/a\\ |1 + cot |-||*|1 + tan |- + --||*tan(a)
|1 + tan |-|| \ \2// \ \2 4 //
\ \2//
$$- \frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}\right) \cot{\left(\frac{a}{2} \right)} \cot{\left(a \right)}}{\left(\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan{\left(a \right)}} + \frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
/ 2/a\\
| 1 - tan |-||
| \2/|
2*|-1 + -----------|
| 2/a\|
2 | 1 + tan |-||
1 1 - tan (a) \ \2//
- - --------------- - ---------------------
2 / 2 \ / 2/a\\ 2
2*\1 + tan (a)/ |1 + tan |-||*tan (a)
\ \2//
$$- \frac{1 - \tan^{2}{\left(a \right)}}{2 \left(\tan^{2}{\left(a \right)} + 1\right)} - \frac{2 \left(\frac{1 - \tan^{2}{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} - 1\right)}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right) \tan^{2}{\left(a \right)}} + \frac{1}{2}$$
/ 2/a pi\\
| cos |- + --||
2 / / pi\\ | \2 4 /| /a\ /a pi\
cos (a)*|1 + cos|a - --||*|-1 + ------------|*cos|-|*cos|- - --|
\ \ 2 // | 2/a pi\| \2/ \2 2 /
| cos |- - --||
1 cos(2*a) \ \2 4 //
- - -------- - ----------------------------------------------------------------
2 2 2/ pi\
cos |a - --|
\ 2 /
$$- \frac{\left(-1 + \frac{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{4} \right)}}\right) \left(\cos{\left(a - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}} - \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2}$$
1 - cos(2*a) 2/a\ 2 / 2/a pi\\ /a\
------------ - cos |-|*cot (a)*(1 + sin(a))*|-1 + cot |- + --||*tan|-|
2 \2/ \ \2 4 // \2/
$$\frac{1 - \cos{\left(2 a \right)}}{2} - \left(\sin{\left(a \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1\right) \cos^{2}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)} \cot^{2}{\left(a \right)}$$
/ 2 \
2/a\ 2 2/pi a\ | cos (a) |
sin |-|*sin (2*a)*sin |-- + -|*(1 + sin(a))*|-1 + --------------|
/pi \ \2/ \2 2/ | 4/a pi\|
sin|-- + 2*a| | 4*sin |- + --||
1 \2 / \ \2 4 //
- - ------------- - -----------------------------------------------------------------
2 2 5
2*sin (a)
$$- \frac{\left(-1 + \frac{\cos^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{4} \right)}}\right) \left(\sin{\left(a \right)} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{2}{\left(2 a \right)} \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{2} \right)}}{2 \sin^{5}{\left(a \right)}} - \frac{\sin{\left(2 a + \frac{\pi}{2} \right)}}{2} + \frac{1}{2}$$
2
1 cos(2*a) 2*cos (a)*(-1 + cos(a))
- - -------- - -------------------------------
2 2 / 2/a pi\\
| cos |- - --||
| \2 2 /| 2/ pi\
|1 + ------------|*cos |a - --|
| 2/a\ | \ 2 /
| cos |-| |
\ \2/ /
$$- \frac{\cos{\left(2 a \right)}}{2} + \frac{1}{2} - \frac{2 \left(\cos{\left(a \right)} - 1\right) \cos^{2}{\left(a \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos^{2}{\left(a - \frac{\pi}{2} \right)}}$$
1/2 - cos(2*a)/2 - 2*cos(a)^2*(-1 + cos(a))/((1 + cos(a/2 - pi/2)^2/cos(a/2)^2)*cos(a - pi/2)^2)
Denominador común
[src]
2 sin(a)*sin(pi - a)
sin (a) - ------------------
tan(a)*tan(pi - a)
$$\sin^{2}{\left(a \right)} - \frac{\sin{\left(a \right)} \sin{\left(\pi - a \right)}}{\tan{\left(a \right)} \tan{\left(\pi - a \right)}}$$
sin(a)^2 - sin(a)*sin(pi - a)/(tan(a)*tan(pi - a))