Sr Examen
¿Cómo vas a descomponer esta sinx/(4-cos^2x) expresión en fracciones?
Solución
Ha introducido
[src]
sin(x)
-----------
2
4 - cos (x)
$$\frac{\sin{\left(x \right)}}{4 - \cos^{2}{\left(x \right)}}$$
sin(x)/(4 - cos(x)^2)
Simplificación general
[src]
-sin(x)
------------
2
-4 + cos (x)
$$- \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)} - 4}$$
-sin(x)/(-4 + cos(x)^2)
Denominador común
[src]
-sin(x)
------------
2
-4 + cos (x)
$$- \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)} - 4}$$
-sin(x)/(-4 + cos(x)^2)
Combinatoria
[src]
-sin(x) -------------------------- (-2 + cos(x))*(2 + cos(x))
$$- \frac{\sin{\left(x \right)}}{\left(\cos{\left(x \right)} - 2\right) \left(\cos{\left(x \right)} + 2\right)}$$
-sin(x)/((-2 + cos(x))*(2 + cos(x)))
Parte trigonométrica
[src]
2 -------------------------- / 1 \ |7 - -------------|*csc(x) | /pi \| | csc|-- - 2*x|| \ \2 //
$$\frac{2}{\left(7 - \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}$$
sin(x)
-----------
2
3 + sin (x)
$$\frac{\sin{\left(x \right)}}{\sin^{2}{\left(x \right)} + 3}$$
sin(x)
----------------
2/ pi\
4 - sin |x + --|
\ 2 /
$$\frac{\sin{\left(x \right)}}{4 - \sin^{2}{\left(x + \frac{\pi}{2} \right)}}$$
/x\
2*cot|-|
\2/
----------------------------------
/ 2/x\ \
| 4*cot |-| |
/ 2/x\\ | \2/ |
|1 + cot |-||*|3 + --------------|
\ \2// | 2|
| / 2/x\\ |
| |1 + cot |-|| |
\ \ \2// /
$$\frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(3 + \frac{4 \cot^{2}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/ pi\
cos|x - --|
\ 2 /
----------------
2/ pi\
3 + cos |x - --|
\ 2 /
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos^{2}{\left(x - \frac{\pi}{2} \right)} + 3}$$
/ pi\
cos|x - --|
\ 2 /
-----------
2
4 - cos (x)
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{4 - \cos^{2}{\left(x \right)}}$$
1 -------------------- / 1 \ |4 - -------|*csc(x) | 2 | \ sec (x)/
$$\frac{1}{\left(4 - \frac{1}{\sec^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}$$
/x\
4*tan|-|
\2/
-------------------------------
/ 2 \
/ 2/x\\ | 1 - tan (x)|
|1 + tan |-||*|7 - -----------|
\ \2// | 2 |
\ 1 + tan (x)/
$$\frac{4 \tan{\left(\frac{x}{2} \right)}}{\left(- \frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 7\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
2 -------------------------- / 1 \ / pi\ |7 - --------|*sec|x - --| \ sec(2*x)/ \ 2 /
$$\frac{2}{\left(7 - \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}$$
2*sin(x) ------------ 7 - cos(2*x)
$$\frac{2 \sin{\left(x \right)}}{7 - \cos{\left(2 x \right)}}$$
1 ------------------------------ / 1 \ / pi\ |3 + ------------|*sec|x - --| | 2/ pi\| \ 2 / | sec |x - --|| \ \ 2 //
$$\frac{1}{\left(3 + \frac{1}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}$$
/x\
2*cot|-|
\2/
-----------------------------------
/ 2\
| / 2/x\\ |
| |-1 + cot |-|| |
/ 2/x\\ | \ \2// |
|1 + cot |-||*|4 - ---------------|
\ \2// | 2|
| / 2/x\\ |
| |1 + cot |-|| |
\ \ \2// /
$$\frac{2 \cot{\left(\frac{x}{2} \right)}}{\left(- \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} + 4\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
2*sin(x)
-----------------
/pi \
7 - sin|-- + 2*x|
\2 /
$$\frac{2 \sin{\left(x \right)}}{7 - \sin{\left(2 x + \frac{\pi}{2} \right)}}$$
1 ------------------------- / 1 \ / pi\ |4 - -------|*sec|x - --| | 2 | \ 2 / \ sec (x)/
$$\frac{1}{\left(4 - \frac{1}{\sec^{2}{\left(x \right)}}\right) \sec{\left(x - \frac{\pi}{2} \right)}}$$
1 -------------------- / 1 \ |3 + -------|*csc(x) | 2 | \ csc (x)/
$$\frac{1}{\left(3 + \frac{1}{\csc^{2}{\left(x \right)}}\right) \csc{\left(x \right)}}$$
/x\
2*tan|-|
\2/
----------------------------------
/ 2\
| / 2/x\\ |
| |1 - tan |-|| |
/ 2/x\\ | \ \2// |
|1 + tan |-||*|4 - --------------|
\ \2// | 2|
| / 2/x\\ |
| |1 + tan |-|| |
\ \ \2// /
$$\frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(- \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} + 4\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/x\
4*cot|-|
\2/
--------------------------------
/ 2 \
/ 2/x\\ | -1 + cot (x)|
|1 + cot |-||*|7 - ------------|
\ \2// | 2 |
\ 1 + cot (x) /
$$\frac{4 \cot{\left(\frac{x}{2} \right)}}{\left(- \frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 7\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/x\
2*tan|-|
\2/
----------------------------------
/ 2/x\ \
| 4*tan |-| |
/ 2/x\\ | \2/ |
|1 + tan |-||*|3 + --------------|
\ \2// | 2|
| / 2/x\\ |
| |1 + tan |-|| |
\ \ \2// /
$$\frac{2 \tan{\left(\frac{x}{2} \right)}}{\left(3 + \frac{4 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/ pi\
2*cos|x - --|
\ 2 /
-------------
7 - cos(2*x)
$$\frac{2 \cos{\left(x - \frac{\pi}{2} \right)}}{7 - \cos{\left(2 x \right)}}$$
1 ------------------------- / 1 \ |4 - ------------|*csc(x) | 2/pi \| | csc |-- - x|| \ \2 //
$$\frac{1}{\left(4 - \frac{1}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}\right) \csc{\left(x \right)}}$$
1/((4 - 1/csc(pi/2 - x)^2)*csc(x))
Potencias
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/ -I*x I*x\ -I*\- e + e / ----------------------- / 2\ | / I*x -I*x\ | | |e e | | 2*|4 - |---- + -----| | \ \ 2 2 / /
$$- \frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(4 - \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}\right)}$$
-i*(-exp(-i*x) + exp(i*x))/(2*(4 - (exp(i*x)/2 + exp(-i*x)/2)^2))