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