Sr Examen
¿Cómo vas a descomponer esta sin(x/2)/(sin(x)*(2cos(x)-1)) expresión en fracciones?
Solución
Ha introducido
[src]
/x\
sin|-|
\2/
---------------------
sin(x)*(2*cos(x) - 1)
$$\frac{\sin{\left(\frac{x}{2} \right)}}{\left(2 \cos{\left(x \right)} - 1\right) \sin{\left(x \right)}}$$
sin(x/2)/((sin(x)*(2*cos(x) - 1)))
Simplificación general
[src]
1
----------
/3*x\
2*cos|---|
\ 2 /
$$\frac{1}{2 \cos{\left(\frac{3 x}{2} \right)}}$$
1/(2*cos(3*x/2))
Respuesta numérica
[src]
sin(x/2)/((-1.0 + 2.0*cos(x))*sin(x))
sin(x/2)/((-1.0 + 2.0*cos(x))*sin(x))
Potencias
[src]
-I*x I*x
----- ---
2 2
- e + e
------------------------------------
/ -I*x I*x\ / I*x -I*x\
\- e + e /*\-1 + e + e /
$$\frac{e^{\frac{i x}{2}} - e^{- \frac{i x}{2}}}{\left(e^{i x} - e^{- i x}\right) \left(e^{i x} - 1 + e^{- i x}\right)}$$
(-exp(-i*x/2) + exp(i*x/2))/((-exp(-i*x) + exp(i*x))*(-1 + exp(i*x) + exp(-i*x)))
Denominador común
[src]
/x\
sin|-|
\2/
-------------------------
-sin(x) + 2*cos(x)*sin(x)
$$\frac{\sin{\left(\frac{x}{2} \right)}}{2 \sin{\left(x \right)} \cos{\left(x \right)} - \sin{\left(x \right)}}$$
sin(x/2)/(-sin(x) + 2*cos(x)*sin(x))
Parte trigonométrica
[src]
/3*x\ sec|---| \ 2 / -------- 2
$$\frac{\sec{\left(\frac{3 x}{2} \right)}}{2}$$
/x\
sin|-|
\2/
---------------------------
/ / pi\\
|-1 + 2*sin|x + --||*sin(x)
\ \ 2 //
$$\frac{\sin{\left(\frac{x}{2} \right)}}{\left(2 \sin{\left(x + \frac{\pi}{2} \right)} - 1\right) \sin{\left(x \right)}}$$
csc(x) -------------------- / 2 \ /x\ |-1 + ------|*csc|-| \ sec(x)/ \2/
$$\frac{\csc{\left(x \right)}}{\left(-1 + \frac{2}{\sec{\left(x \right)}}\right) \csc{\left(\frac{x}{2} \right)}}$$
/pi 3*x\
csc|-- - ---|
\2 2 /
-------------
2
$$\frac{\csc{\left(- \frac{3 x}{2} + \frac{\pi}{2} \right)}}{2}$$
2/3*x\
1 + cot |---|
\ 4 /
------------------
/ 2/3*x\\
2*|-1 + cot |---||
\ \ 4 //
$$\frac{\cot^{2}{\left(\frac{3 x}{4} \right)} + 1}{2 \left(\cot^{2}{\left(\frac{3 x}{4} \right)} - 1\right)}$$
/ 2/x\\ /x\
|1 + cot |-||*cot|-|
\ \2// \4/
--------------------------------------------
/ / 2/x\\\
| 2*|-1 + cot |-|||
/ 2/x\\ | \ \2//| /x\
|1 + cot |-||*|-1 + ----------------|*cot|-|
\ \4// | 2/x\ | \2/
| 1 + cot |-| |
\ \2/ /
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(\frac{x}{4} \right)}}{\left(\frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} - 1\right) \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}$$
1
---------------
/pi 3*x\
2*sin|-- + ---|
\2 2 /
$$\frac{1}{2 \sin{\left(\frac{3 x}{2} + \frac{\pi}{2} \right)}}$$
/x\
sin|-|
\2/
------------------
-sin(x) + sin(2*x)
$$\frac{\sin{\left(\frac{x}{2} \right)}}{- \sin{\left(x \right)} + \sin{\left(2 x \right)}}$$
csc(x) ------------------------- / 2 \ /x\ |-1 + -----------|*csc|-| | /pi \| \2/ | csc|-- - x|| \ \2 //
$$\frac{\csc{\left(x \right)}}{\left(-1 + \frac{2}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(\frac{x}{2} \right)}}$$
2/3*x\
1 + tan |---|
\ 4 /
-----------------
/ 2/3*x\\
2*|1 - tan |---||
\ \ 4 //
$$\frac{\tan^{2}{\left(\frac{3 x}{4} \right)} + 1}{2 \left(1 - \tan^{2}{\left(\frac{3 x}{4} \right)}\right)}$$
/ 2/x\\ /x\
|1 + tan |-||*tan|-|
\ \2// \4/
-------------------------------------------
/ / 2/x\\\
| 2*|1 - tan |-|||
/ 2/x\\ | \ \2//| /x\
|1 + tan |-||*|-1 + ---------------|*tan|-|
\ \4// | 2/x\ | \2/
| 1 + tan |-| |
\ \2/ /
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(\frac{x}{4} \right)}}{\left(\frac{2 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} - 1\right) \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right) \tan{\left(\frac{x}{2} \right)}}$$
1
----------
/3*x\
2*cos|---|
\ 2 /
$$\frac{1}{2 \cos{\left(\frac{3 x}{2} \right)}}$$
/ pi\
sec|x - --|
\ 2 /
-------------------------
/ 2 \ /x pi\
|-1 + ------|*sec|- - --|
\ sec(x)/ \2 2 /
$$\frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\left(-1 + \frac{2}{\sec{\left(x \right)}}\right) \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}$$
/x pi\
cos|- - --|
\2 2 /
---------------------------
/ pi\
(-1 + 2*cos(x))*cos|x - --|
\ 2 /
$$\frac{\cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(2 \cos{\left(x \right)} - 1\right) \cos{\left(x - \frac{\pi}{2} \right)}}$$
cos(x/2 - pi/2)/((-1 + 2*cos(x))*cos(x - pi/2))