Sr Examen
¿Cómo vas a descomponer esta (sin2x)/(2*cos^2x) expresión en fracciones?
Solución
Ha introducido
[src]
sin(2*x)
---------
2
2*cos (x)
$$\frac{\sin{\left(2 x \right)}}{2 \cos^{2}{\left(x \right)}}$$
sin(2*x)/((2*cos(x)^2))
Parte trigonométrica
[src]
/ pi\ cos|2*x - --| \ 2 / ------------- 1 + cos(2*x)
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{\cos{\left(2 x \right)} + 1}$$
2
sec (x)
---------------
/ pi\
2*sec|2*x - --|
\ 2 /
$$\frac{\sec^{2}{\left(x \right)}}{2 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
/pi \ csc|-- - x| \2 / ----------- csc(x)
$$\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{\csc{\left(x \right)}}$$
2*cot(x)
--------------------------------
/ 2 \
/ 2 \ | -1 + cot (x)|
\1 + cot (x)/*|1 + ------------|
| 2 |
\ 1 + cot (x) /
$$\frac{2 \cot{\left(x \right)}}{\left(\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}$$
/ pi\ cos|x - --| \ 2 / ----------- cos(x)
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{\cos{\left(x \right)}}$$
sin(2*x)
-----------------
/pi \
1 + sin|-- + 2*x|
\2 /
$$\frac{\sin{\left(2 x \right)}}{\sin{\left(2 x + \frac{\pi}{2} \right)} + 1}$$
tan(x)
$$\tan{\left(x \right)}$$
2
/ 2/x\\
|1 + cot |-|| *cot(x)
\ \2//
-----------------------------
2
/ 2 \ / 2/x\\
\1 + cot (x)/*|-1 + cot |-||
\ \2//
$$\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \cot{\left(x \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right)}$$
sin(2*x)
--------------
2/ pi\
2*sin |x + --|
\ 2 /
$$\frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x + \frac{\pi}{2} \right)}}$$
2 sec (x) ---------- 2*csc(2*x)
$$\frac{\sec^{2}{\left(x \right)}}{2 \csc{\left(2 x \right)}}$$
2
/ 2/x\\
|1 + tan |-|| *tan(x)
\ \2//
----------------------------
2
/ 2 \ / 2/x\\
\1 + tan (x)/*|1 - tan |-||
\ \2//
$$\frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \tan{\left(x \right)}}{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}$$
1 ------ cot(x)
$$\frac{1}{\cot{\left(x \right)}}$$
/ pi\
cos|2*x - --|
\ 2 /
-------------
2
2*cos (x)
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{2 \cos^{2}{\left(x \right)}}$$
1 ---------------------------- / 1 \ / pi\ |1 + --------|*sec|2*x - --| \ sec(2*x)/ \ 2 /
$$\frac{1}{\left(1 + \frac{1}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
sin(2*x) ------------ 1 + cos(2*x)
$$\frac{\sin{\left(2 x \right)}}{\cos{\left(2 x \right)} + 1}$$
1 ---------------------------- / 1 \ |1 + -------------|*csc(2*x) | /pi \| | csc|-- - 2*x|| \ \2 //
$$\frac{1}{\left(1 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}\right) \csc{\left(2 x \right)}}$$
2*tan(x)
-------------------------------
/ 2 \
/ 2 \ | 1 - tan (x)|
\1 + tan (x)/*|1 + -----------|
| 2 |
\ 1 + tan (x)/
$$\frac{2 \tan{\left(x \right)}}{\left(\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}$$
2/pi \
csc |-- - x|
\2 /
------------
2*csc(2*x)
$$\frac{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}}{2 \csc{\left(2 x \right)}}$$
2 2*sin (x) --------- sin(2*x)
$$\frac{2 \sin^{2}{\left(x \right)}}{\sin{\left(2 x \right)}}$$
sec(x) ----------- / pi\ sec|x - --| \ 2 /
$$\frac{\sec{\left(x \right)}}{\sec{\left(x - \frac{\pi}{2} \right)}}$$
sec(x)/sec(x - pi/2)
Potencias
[src]
/ -2*I*x 2*I*x\
-I*\- e + e /
------------------------
2
/ I*x -I*x\
|e e |
4*|---- + -----|
\ 2 2 /
$$- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{4 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}$$
-i*(-exp(-2*i*x) + exp(2*i*x))/(4*(exp(i*x)/2 + exp(-i*x)/2)^2)