Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(a)*(-cos(a))*(-cos(2*a))/((cos(4)*a))
¿Cómo vas a descomponer esta sin(a)*(-cos(a))*(-cos(2*a))/((cos(4)*a)) expresión en fracciones?
Solución
Ha introducido
[src]
sin(a)*(-cos(a))*(-cos(2*a))
----------------------------
cos(4)*a
$$\frac{\sin{\left(a \right)} \left(- \cos{\left(a \right)}\right) \left(- \cos{\left(2 a \right)}\right)}{a \cos{\left(4 \right)}}$$
((sin(a)*(-cos(a)))*(-cos(2*a)))/((cos(4)*a))
Simplificación general
[src]
sin(4*a) ---------- 4*a*cos(4)
$$\frac{\sin{\left(4 a \right)}}{4 a \cos{\left(4 \right)}}$$
sin(4*a)/(4*a*cos(4))
Respuesta numérica
[src]
-1.5298856564664*cos(a)*cos(2*a)*sin(a)/a
-1.5298856564664*cos(a)*cos(2*a)*sin(a)/a
Denominador común
[src]
cos(a)*cos(2*a)*sin(a)
----------------------
a*cos(4)
$$\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}}$$
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Combinatoria
[src]
cos(a)*cos(2*a)*sin(a)
----------------------
a*cos(4)
$$\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}}$$
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Denominador racional
[src]
cos(a)*cos(2*a)*sin(a)
----------------------
a*cos(4)
$$\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}}$$
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Unión de expresiones racionales
[src]
cos(a)*cos(2*a)*sin(a)
----------------------
a*cos(4)
$$\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}}$$
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Compilar la expresión
[src]
cos(a)*cos(2*a)*sin(a)
----------------------
a*cos(4)
$$\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}}$$
cos(a)*cos(2*a)*sin(a)/(a*cos(4))
Parte trigonométrica
[src]
2 4/a\ / 2 \ / 2/a\\ /a\
2*cos (a)*cos |-|*\1 - tan (a)/*|1 - tan |-||*tan|-|
\2/ \ \2// \2/
----------------------------------------------------
/ 2 \ 2
a*\1 - tan (2)/*cos (2)
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(1 - \tan^{2}{\left(a \right)}\right) \cos^{4}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)} \tan{\left(\frac{a}{2} \right)}}{a \left(1 - \tan^{2}{\left(2 \right)}\right) \cos^{2}{\left(2 \right)}}$$
/ pi\ csc|-4 + --| \ 2 / ------------ 4*a*csc(4*a)
$$\frac{\csc{\left(-4 + \frac{\pi}{2} \right)}}{4 a \csc{\left(4 a \right)}}$$
2 4/a\ / 2 \ / 2/a\\ /a\
2*sin (a)*sin |-|*\-1 + cot (a)/*|-1 + cot |-||*cot|-|
\2/ \ \2// \2/
------------------------------------------------------
/ 2 \ 2
a*\-1 + cot (2)/*sin (2)
$$\frac{2 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(a \right)} - 1\right) \sin^{4}{\left(\frac{a}{2} \right)} \sin^{2}{\left(a \right)} \cot{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(2 \right)}\right) \sin^{2}{\left(2 \right)}}$$
/ 2/a\ \
/ 2 \ | cos |-| |
2/ pi\ 3/a pi\ | cos (a) | | \2/ | /a\
2*cos |a - --|*cos |- - --|*|-1 + ------------|*|-1 + ------------|*cos|-|
\ 2 / \2 2 / | 2/ pi\| | 2/a pi\| \2/
| cos |a - --|| | cos |- - --||
\ \ 2 // \ \2 2 //
--------------------------------------------------------------------------
/ 2 \
| cos (2) | 2/ pi\
a*|-1 + ------------|*cos |2 - --|
| 2/ pi\| \ 2 /
| cos |2 - --||
\ \ 2 //
$$\frac{2 \left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} - 1\right) \left(\frac{\cos^{2}{\left(a \right)}}{\cos^{2}{\left(a - \frac{\pi}{2} \right)}} - 1\right) \cos{\left(\frac{a}{2} \right)} \cos^{3}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{a \left(-1 + \frac{\cos^{2}{\left(2 \right)}}{\cos^{2}{\left(2 - \frac{\pi}{2} \right)}}\right) \cos^{2}{\left(2 - \frac{\pi}{2} \right)}}$$
sin(4*a)
---------------
/ pi\
4*a*sin|4 + --|
\ 2 /
$$\frac{\sin{\left(4 a \right)}}{4 a \sin{\left(\frac{\pi}{2} + 4 \right)}}$$
2
/ 2 \ 4/a\ / 1 \ / 1 \ /a\
32*\1 + tan (1)/ *tan |-|*|-1 + -------|*|-1 + -------|*tan|-|
\4/ | 2 | | 2/a\| \2/
\ tan (a)/ | tan |-||
\ \2//
--------------------------------------------------------------
2 4
/ 2/a\\ / 2/a\\ / 1 \ 2
a*|1 + tan |-|| *|1 + tan |-|| *|-1 + -------|*tan (1)
\ \2// \ \4// | 2 |
\ tan (2)/
$$\frac{32 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \tan^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} \right)}}{a \left(-1 + \frac{1}{\tan^{2}{\left(2 \right)}}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan^{2}{\left(1 \right)}}$$
sin(4*a) ---------- 4*a*cos(4)
$$\frac{\sin{\left(4 a \right)}}{4 a \cos{\left(4 \right)}}$$
/ 2 \
3 2/a\ / 1 \ | sin (a) |
sin (a)*sin |-|*|-1 + -------|*|-1 + ---------|
\2/ | 2 | | 4/a\|
\ tan (a)/ | 4*sin |-||
\ \2//
-----------------------------------------------
/ 2 \
| sin (4) | 2
a*|-1 + ---------|*sin (2)
| 4 |
\ 4*sin (2)/
$$\frac{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{3}{\left(a \right)}}{a \left(-1 + \frac{\sin^{2}{\left(4 \right)}}{4 \sin^{4}{\left(2 \right)}}\right) \sin^{2}{\left(2 \right)}}$$
sec(4) ------------------------ a*csc(a)*sec(a)*sec(2*a)
$$\frac{\sec{\left(4 \right)}}{a \csc{\left(a \right)} \sec{\left(a \right)} \sec{\left(2 a \right)}}$$
/ 2 \
\1 + cot (2)/*cot(2*a)
----------------------------------
/ 2 \ / 2 \
2*a*\1 + cot (2*a)/*\-1 + cot (2)/
$$\frac{\left(\cot^{2}{\left(2 \right)} + 1\right) \cot{\left(2 a \right)}}{2 a \left(-1 + \cot^{2}{\left(2 \right)}\right) \left(\cot^{2}{\left(2 a \right)} + 1\right)}$$
/ 4/a\\
| 4*sin |-|| / 4 \
2/a\ 2/ pi\ 4/pi a\ | \2/| | 4*sin (a)|
4*sin |-|*sin |a + --|*sin |-- + -|*|1 - ---------|*|1 - ---------|
\2/ \ 2 / \2 2/ | 2 | | 2 |
\ sin (a) / \ sin (2*a)/
-------------------------------------------------------------------
/ 4 \
| 4*sin (2)| 2/ pi\
a*|1 - ---------|*sin(a)*sin |2 + --|
| 2 | \ 2 /
\ sin (4) /
$$\frac{4 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{2} \right)} \sin^{2}{\left(a + \frac{\pi}{2} \right)}}{a \left(- \frac{4 \sin^{4}{\left(2 \right)}}{\sin^{2}{\left(4 \right)}} + 1\right) \sin{\left(a \right)} \sin^{2}{\left(\frac{\pi}{2} + 2 \right)}}$$
/ pi\
cos(a)*cos(2*a)*cos|a - --|
\ 2 /
---------------------------
a*cos(4)
$$\frac{\cos{\left(a \right)} \cos{\left(2 a \right)} \cos{\left(a - \frac{\pi}{2} \right)}}{a \cos{\left(4 \right)}}$$
/ 4/a\\
| 4*sin |-||
2 4/a\ 2/a\ / 2 \ | \2/|
4*cos (a)*cos |-|*sin |-|*\1 - tan (a)/*|1 - ---------|
\2/ \2/ | 2 |
\ sin (a) /
-------------------------------------------------------
/ 4 \
| 4*sin (2)| 2
a*|1 - ---------|*cos (2)*sin(a)
| 2 |
\ sin (4) /
$$\frac{4 \left(1 - \tan^{2}{\left(a \right)}\right) \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \sin^{2}{\left(\frac{a}{2} \right)} \cos^{4}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)}}{a \left(- \frac{4 \sin^{4}{\left(2 \right)}}{\sin^{2}{\left(4 \right)}} + 1\right) \sin{\left(a \right)} \cos^{2}{\left(2 \right)}}$$
/ 2/pi \\ / 2/pi a\\
| csc |-- - a|| | csc |-- - -||
2/ pi\ | \2 /| | \2 2/|
2*csc |-2 + --|*|1 - ------------|*|1 - ------------|
\ 2 / | 2 | | 2/a\ |
\ csc (a) / | csc |-| |
\ \2/ /
------------------------------------------------------
/ 2/ pi\\
| csc |-2 + --||
| \ 2 /| /a\ 2/pi \ 3/pi a\
a*|1 - -------------|*csc|-|*csc |-- - a|*csc |-- - -|
| 2 | \2/ \2 / \2 2/
\ csc (2) /
$$\frac{2 \left(1 - \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 - \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}\right) \csc^{2}{\left(-2 + \frac{\pi}{2} \right)}}{a \left(- \frac{\csc^{2}{\left(-2 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(2 \right)}} + 1\right) \csc{\left(\frac{a}{2} \right)} \csc^{2}{\left(- a + \frac{\pi}{2} \right)} \csc^{3}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}$$
/ 2/a\ \
/ 2 \ | sec |-| |
2 | sec (a) | | \2/ |
2*sec (2)*|1 - ------------|*|1 - ------------|
| 2/ pi\| | 2/a pi\|
| sec |a - --|| | sec |- - --||
\ \ 2 // \ \2 2 //
------------------------------------------------
/ 2 \
| sec (2) | 2 3/a\ /a pi\
a*|1 - ------------|*sec (a)*sec |-|*sec|- - --|
| 2/ pi\| \2/ \2 2 /
| sec |2 - --||
\ \ 2 //
$$\frac{2 \left(- \frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \left(- \frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec^{2}{\left(2 \right)}}{a \left(- \frac{\sec^{2}{\left(2 \right)}}{\sec^{2}{\left(2 - \frac{\pi}{2} \right)}} + 1\right) \sec^{3}{\left(\frac{a}{2} \right)} \sec^{2}{\left(a \right)} \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
2
/ 2 \ 4/a\ 8/a\ 4/a\ / 1 \ / 1 \ / 1 \ /a\
16*\1 + tan (1)/ *cos |-|*cos |-|*tan |-|*|-1 + ------|*|-1 + -------|*|-1 + -------|*tan|-|
\2/ \4/ \4/ \ cos(4)/ | 2 | | 2/a\| \2/
\ tan (a)/ | tan |-||
\ \2//
--------------------------------------------------------------------------------------------
2
a*tan (1)
$$\frac{16 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \left(\frac{1}{\cos{\left(4 \right)}} - 1\right) \cos^{8}{\left(\frac{a}{4} \right)} \cos^{4}{\left(\frac{a}{2} \right)} \tan^{4}{\left(\frac{a}{4} \right)} \tan{\left(\frac{a}{2} \right)}}{a \tan^{2}{\left(1 \right)}}$$
3/a\ 4/a\ 4/a\ 8/a\ 2 / 2 \ / 2/a\\
32*cot |-|*cot |-|*sin |-|*sin |-|*tan (1)*\-1 + cot (a)/*|-1 + cot |-||
\2/ \4/ \2/ \4/ \ \2//
------------------------------------------------------------------------
/ 2 \ 4
a*\-1 + cot (2)/*sin (1)
$$\frac{32 \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(a \right)} - 1\right) \sin^{8}{\left(\frac{a}{4} \right)} \sin^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(1 \right)} \cot^{4}{\left(\frac{a}{4} \right)} \cot^{3}{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(2 \right)}\right) \sin^{4}{\left(1 \right)}}$$
2 3 4
/ 2 \ / 2/a\\ / 2/a\\ 4/a\ 8/a\ / 2 \ /a\
2*\1 + tan (1)/ *|1 - tan |-|| *|1 - tan |-|| *cos |-|*cos |-|*\1 - tan (a)/*tan|-|
\ \2// \ \4// \2/ \4/ \2/
-----------------------------------------------------------------------------------
2
/ 2 \ / 2 \
a*\1 - tan (1)/ *\1 - tan (2)/
$$\frac{2 \left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{3} \left(1 - \tan^{2}{\left(a \right)}\right) \cos^{8}{\left(\frac{a}{4} \right)} \cos^{4}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)}}{a \left(1 - \tan^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 \right)}\right)}$$
2 2 4
/ 2 \ / 2/a\\ / 2/a\\ / 1 \ / 1 \
2*\1 + cot (1)/ *|-1 + cot |-|| *|-1 + cot |-|| *|1 - -------|*|1 - -------|
\ \2// \ \4// | 2 | | 2/a\|
\ cot (a)/ | cot |-||
\ \2//
----------------------------------------------------------------------------
2 4 2
/ 2/a\\ / 2/a\\ / 1 \ / 2 \ /a\
a*|1 + cot |-|| *|1 + cot |-|| *|1 - -------|*\-1 + cot (1)/ *cot|-|
\ \2// \ \4// | 2 | \2/
\ cot (2)/
$$\frac{2 \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 - \frac{1}{\cot^{2}{\left(a \right)}}\right) \left(\cot^{2}{\left(1 \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2}}{a \left(-1 + \cot^{2}{\left(1 \right)}\right)^{2} \left(1 - \frac{1}{\cot^{2}{\left(2 \right)}}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot{\left(\frac{a}{2} \right)}}$$
/ pi\
csc|-4 + --|
\ 2 /
----------------------------------
/pi \ /pi \
a*csc(a)*csc|-- - a|*csc|-- - 2*a|
\2 / \2 /
$$\frac{\csc{\left(-4 + \frac{\pi}{2} \right)}}{a \csc{\left(a \right)} \csc{\left(- 2 a + \frac{\pi}{2} \right)} \csc{\left(- a + \frac{\pi}{2} \right)}}$$
sec(4)
-----------------
/ pi\
4*a*sec|4*a - --|
\ 2 /
$$\frac{\sec{\left(4 \right)}}{4 a \sec{\left(4 a - \frac{\pi}{2} \right)}}$$
/ 2/a\ \
/ 2 \ | csc |-| |
2 | csc (a) | | \2/ |
2*csc (2)*|-1 + ------------|*|-1 + ------------|
| 2/pi \| | 2/pi a\|
| csc |-- - a|| | csc |-- - -||
\ \2 // \ \2 2//
--------------------------------------------------
/ 2 \
| csc (2) | 2 3/a\ /pi a\
a*|-1 + -------------|*csc (a)*csc |-|*csc|-- - -|
| 2/ pi\| \2/ \2 2/
| csc |-2 + --||
\ \ 2 //
$$\frac{2 \left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} - 1\right) \left(\frac{\csc^{2}{\left(a \right)}}{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}} - 1\right) \csc^{2}{\left(2 \right)}}{a \left(-1 + \frac{\csc^{2}{\left(2 \right)}}{\csc^{2}{\left(-2 + \frac{\pi}{2} \right)}}\right) \csc^{3}{\left(\frac{a}{2} \right)} \csc^{2}{\left(a \right)} \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}$$
cos(a)*cos(2*a)*sin(a)
----------------------
a*cos(4)
$$\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}}$$
2 3 4
/ 2 \ / 2/a\\ / 2/a\\ / 2 \ /a\
2*\1 + tan (1)/ *|1 - tan |-|| *|1 - tan |-|| *\1 - tan (a)/*tan|-|
\ \2// \ \4// \2/
-------------------------------------------------------------------
2 4 2
/ 2/a\\ / 2/a\\ / 2 \ / 2 \
a*|1 + tan |-|| *|1 + tan |-|| *\1 - tan (1)/ *\1 - tan (2)/
\ \2// \ \4//
$$\frac{2 \left(1 + \tan^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(\frac{a}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right)^{3} \left(1 - \tan^{2}{\left(a \right)}\right) \tan{\left(\frac{a}{2} \right)}}{a \left(1 - \tan^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 \right)}\right) \left(\tan^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
2
/ 2 \ 3/a\ 4/a\ / 2 \ / 2/a\\
32*\1 + cot (1)/ *cot |-|*cot |-|*\-1 + cot (a)/*|-1 + cot |-||
\2/ \4/ \ \2//
---------------------------------------------------------------
2 4
/ 2/a\\ / 2/a\\ / 2 \ 2
a*|1 + cot |-|| *|1 + cot |-|| *\-1 + cot (2)/*cot (1)
\ \2// \ \4//
$$\frac{32 \left(\cot^{2}{\left(1 \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(a \right)} - 1\right) \cot^{4}{\left(\frac{a}{4} \right)} \cot^{3}{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(2 \right)}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} + 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot^{2}{\left(1 \right)}}$$
2 2 3/a\ / 1 \ / 1 \ / 1 \ /a\
csc (2)*sin (a)*sin |-|*|-1 + ------|*|-1 + -------|*|-1 + -------|*cos|-|
\2/ \ cos(4)/ | 2 | | 2/a\| \2/
\ tan (a)/ | tan |-||
\ \2//
--------------------------------------------------------------------------
a
$$\frac{\left(-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \left(\frac{1}{\cos{\left(4 \right)}} - 1\right) \sin^{3}{\left(\frac{a}{2} \right)} \sin^{2}{\left(a \right)} \cos{\left(\frac{a}{2} \right)} \csc^{2}{\left(2 \right)}}{a}$$
/ 2 \ / 2 \ / 2/a\\ /a\
2*\1 + cot (2)/*\-1 + cot (a)/*|-1 + cot |-||*cot|-|
\ \2// \2/
----------------------------------------------------
2
/ 2 \ / 2/a\\ / 2 \
a*\1 + cot (a)/*|1 + cot |-|| *\-1 + cot (2)/
\ \2//
$$\frac{2 \left(\cot^{2}{\left(2 \right)} + 1\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right) \left(\cot^{2}{\left(a \right)} - 1\right) \cot{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(2 \right)}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\cot^{2}{\left(a \right)} + 1\right)}$$
2 4
/ 2/a\\ / 2/a\\ 4/a\ 8/a\ / 2 \ / 2/a\\ /a\
2*|-1 + cot |-|| *|-1 + cot |-|| *sin |-|*sin |-|*\1 - tan (a)/*|1 - tan |-||*tan|-|
\ \2// \ \4// \2/ \4/ \ \2// \2/
------------------------------------------------------------------------------------
2
/ 2 \ / 2 \ 4
a*\1 - tan (2)/*\-1 + cot (1)/ *sin (1)
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(1 - \tan^{2}{\left(a \right)}\right) \left(\cot^{2}{\left(\frac{a}{4} \right)} - 1\right)^{4} \left(\cot^{2}{\left(\frac{a}{2} \right)} - 1\right)^{2} \sin^{8}{\left(\frac{a}{4} \right)} \sin^{4}{\left(\frac{a}{2} \right)} \tan{\left(\frac{a}{2} \right)}}{a \left(-1 + \cot^{2}{\left(1 \right)}\right)^{2} \left(1 - \tan^{2}{\left(2 \right)}\right) \sin^{4}{\left(1 \right)}}$$
/ 2 \ / 2 \
3 2/a\ | sin (2*a)| | sin (a) |
sin (a)*sin |-|*|-1 + ---------|*|-1 + ---------|
\2/ | 4 | | 4/a\|
\ 4*sin (a)/ | 4*sin |-||
\ \2//
-------------------------------------------------
/ 2 \
| sin (4) | 2
a*|-1 + ---------|*sin (2)
| 4 |
\ 4*sin (2)/
$$\frac{\left(-1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{\sin^{2}{\left(2 a \right)}}{4 \sin^{4}{\left(a \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)} \sin^{3}{\left(a \right)}}{a \left(-1 + \frac{\sin^{2}{\left(4 \right)}}{4 \sin^{4}{\left(2 \right)}}\right) \sin^{2}{\left(2 \right)}}$$
2 3/a\ 2 / 2 \ / 2/a\\ /a\
2*cos (a)*cos |-|*sec (2)*\1 - tan (a)/*|1 - tan |-||*sin|-|
\2/ \ \2// \2/
------------------------------------------------------------
/ 2 \
a*\1 - tan (2)/
$$\frac{2 \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(\frac{a}{2} \right)} \cos^{3}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)} \sec^{2}{\left(2 \right)}}{a \left(1 - \tan^{2}{\left(2 \right)}\right)}$$
/ 2 \ / 2 \ / 2/a\\ /a\
2*\1 + tan (2)/*\1 - tan (a)/*|1 - tan |-||*tan|-|
\ \2// \2/
--------------------------------------------------
2
/ 2 \ / 2/a\\ / 2 \
a*\1 + tan (a)/*|1 + tan |-|| *\1 - tan (2)/
\ \2//
$$\frac{2 \left(1 + \tan^{2}{\left(2 \right)}\right) \left(1 - \tan^{2}{\left(\frac{a}{2} \right)}\right) \left(1 - \tan^{2}{\left(a \right)}\right) \tan{\left(\frac{a}{2} \right)}}{a \left(1 - \tan^{2}{\left(2 \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \left(\tan^{2}{\left(a \right)} + 1\right)}$$
/ 2/ pi\\ / 2/a pi\\
| cos |a - --|| | cos |- - --||
2 3/a\ | \ 2 /| | \2 2 /| /a pi\
2*cos (a)*cos |-|*|1 - ------------|*|1 - ------------|*cos|- - --|
\2/ | 2 | | 2/a\ | \2 2 /
\ cos (a) / | cos |-| |
\ \2/ /
-------------------------------------------------------------------
/ 2/ pi\\
| cos |2 - --||
| \ 2 /| 2
a*|1 - ------------|*cos (2)
| 2 |
\ cos (2) /
$$\frac{2 \left(1 - \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \left(1 - \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}\right) \cos^{3}{\left(\frac{a}{2} \right)} \cos^{2}{\left(a \right)} \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{a \left(- \frac{\cos^{2}{\left(2 - \frac{\pi}{2} \right)}}{\cos^{2}{\left(2 \right)}} + 1\right) \cos^{2}{\left(2 \right)}}$$
/ pi\ cos|4*a - --| \ 2 / ------------- 4*a*cos(4)
$$\frac{\cos{\left(4 a - \frac{\pi}{2} \right)}}{4 a \cos{\left(4 \right)}}$$
3 3/a\ / 2 \ /a\
4*cos (a)*cos |-|*\1 - tan (a)/*sin|-|
\2/ \2/
--------------------------------------
/ 2 \ 2
a*\1 - tan (2)/*(1 + cos(a))*cos (2)
$$\frac{4 \left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(\frac{a}{2} \right)} \cos^{3}{\left(\frac{a}{2} \right)} \cos^{3}{\left(a \right)}}{a \left(1 - \tan^{2}{\left(2 \right)}\right) \left(\cos{\left(a \right)} + 1\right) \cos^{2}{\left(2 \right)}}$$
sec(4)*sin(4*a)
---------------
4*a
$$\frac{\sin{\left(4 a \right)} \sec{\left(4 \right)}}{4 a}$$
/ 2/ pi\\ / 2/a pi\\
| sec |a - --|| | sec |- - --||
2/ pi\ | \ 2 /| | \2 2 /|
2*sec |2 - --|*|-1 + ------------|*|-1 + ------------|
\ 2 / | 2 | | 2/a\ |
\ sec (a) / | sec |-| |
\ \2/ /
------------------------------------------------------
/ 2/ pi\\
| sec |2 - --||
| \ 2 /| /a\ 2/ pi\ 3/a pi\
a*|-1 + ------------|*sec|-|*sec |a - --|*sec |- - --|
| 2 | \2/ \ 2 / \2 2 /
\ sec (2) /
$$\frac{2 \left(-1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \left(-1 + \frac{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(a \right)}}\right) \sec^{2}{\left(2 - \frac{\pi}{2} \right)}}{a \left(-1 + \frac{\sec^{2}{\left(2 - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 \right)}}\right) \sec{\left(\frac{a}{2} \right)} \sec^{3}{\left(\frac{a}{2} - \frac{\pi}{2} \right)} \sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$
2 3/a\ / 1 \ / 1 \ /a\
-2*sin (a)*sin |-|*|-1 + ------|*|-1 + -------|*cos(a)*cos|-|
\2/ \ cos(4)/ | 2 | \2/
\ tan (a)/
-------------------------------------------------------------
2
a*(-1 + cos(a))*sin (2)
$$- \frac{2 \left(-1 + \frac{1}{\tan^{2}{\left(a \right)}}\right) \left(\frac{1}{\cos{\left(4 \right)}} - 1\right) \sin^{3}{\left(\frac{a}{2} \right)} \sin^{2}{\left(a \right)} \cos{\left(\frac{a}{2} \right)} \cos{\left(a \right)}}{a \left(\cos{\left(a \right)} - 1\right) \sin^{2}{\left(2 \right)}}$$
/ pi\ /pi \
sin(a)*sin|a + --|*sin|-- + 2*a|
\ 2 / \2 /
--------------------------------
/ pi\
a*sin|4 + --|
\ 2 /
$$\frac{\sin{\left(a \right)} \sin{\left(a + \frac{\pi}{2} \right)} \sin{\left(2 a + \frac{\pi}{2} \right)}}{a \sin{\left(\frac{\pi}{2} + 4 \right)}}$$
sec(4)
-----------------------------
/ pi\
a*sec(a)*sec(2*a)*sec|a - --|
\ 2 /
$$\frac{\sec{\left(4 \right)}}{a \sec{\left(a \right)} \sec{\left(2 a \right)} \sec{\left(a - \frac{\pi}{2} \right)}}$$
/ 2 \
\1 + tan (2)/*tan(2*a)
---------------------------------
/ 2 \ / 2 \
2*a*\1 + tan (2*a)/*\1 - tan (2)/
$$\frac{\left(1 + \tan^{2}{\left(2 \right)}\right) \tan{\left(2 a \right)}}{2 a \left(1 - \tan^{2}{\left(2 \right)}\right) \left(\tan^{2}{\left(2 a \right)} + 1\right)}$$
(1 + tan(2)^2)*tan(2*a)/(2*a*(1 + tan(2*a)^2)*(1 - tan(2)^2))
Potencias
[src]
cos(a)*cos(2*a)*sin(a)
----------------------
a*cos(4)
$$\frac{\sin{\left(a \right)} \cos{\left(a \right)} \cos{\left(2 a \right)}}{a \cos{\left(4 \right)}}$$
/ I*a -I*a\ / -2*I*a 2*I*a\
/ -I*a I*a\ | e e | | e e |
-I*\- e + e /*|- ---- - -----|*|- ------- - ------|
\ 2 2 / \ 2 2 /
----------------------------------------------------------
/ -4*I 4*I\
|e e |
2*a*|----- + ----|
\ 2 2 /
$$- \frac{i \left(- \frac{e^{i a}}{2} - \frac{e^{- i a}}{2}\right) \left(e^{i a} - e^{- i a}\right) \left(- \frac{e^{2 i a}}{2} - \frac{e^{- 2 i a}}{2}\right)}{2 a \left(\frac{e^{4 i}}{2} + \frac{e^{- 4 i}}{2}\right)}$$
-i*(-exp(-i*a) + exp(i*a))*(-exp(i*a)/2 - exp(-i*a)/2)*(-exp(-2*i*a)/2 - exp(2*i*a)/2)/(2*a*(exp(-4*i)/2 + exp(4*i)/2))