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