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