Sr Examen
¿Cómo vas a descomponer esta cos(x)/(2*sqrt(1+sin(x))) expresión en fracciones?
Solución
Ha introducido
[src]
cos(x)
----------------
____________
2*\/ 1 + sin(x)
$$\frac{\cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}}$$
cos(x)/((2*sqrt(1 + sin(x))))
Potencias
[src]
I*x -I*x
e e
---- + -----
2 2
-------------------------------
________________________
/ / -I*x I*x\
/ I*\- e + e /
2* / 1 - ------------------
\/ 2
$$\frac{\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}}{2 \sqrt{- \frac{i \left(e^{i x} - e^{- i x}\right)}{2} + 1}}$$
(exp(i*x)/2 + exp(-i*x)/2)/(2*sqrt(1 - i*(-exp(-i*x) + exp(i*x))/2))
Denominador racional
[src]
____________
\/ 1 + sin(x) *cos(x)
---------------------
2 + 2*sin(x)
$$\frac{\sqrt{\sin{\left(x \right)} + 1} \cos{\left(x \right)}}{2 \sin{\left(x \right)} + 2}$$
sqrt(1 + sin(x))*cos(x)/(2 + 2*sin(x))
Parte trigonométrica
[src]
2/x\
8*cot |-|
\4/
1 - --------------
2
/ 2/x\\
|1 + cot |-||
\ \4//
---------------------------
_________________
/ /x\
/ 2*cot|-|
/ \2/
2* / 1 + -----------
/ 2/x\
/ 1 + cot |-|
\/ \2/
$$\frac{1 - \frac{8 \cot^{2}{\left(\frac{x}{4} \right)}}{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}}{2 \sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}}}$$
2
1 - ------------
2/x pi\
sec |- - --|
\2 2 /
-------------------------
_________________
/ 1
2* / 1 + -----------
/ / pi\
/ sec|x - --|
\/ \ 2 /
$$\frac{1 - \frac{2}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}}{2 \sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}}}$$
1
-------------------------
____________
/ 1
2* / 1 + ------ *sec(x)
\/ csc(x)
$$\frac{1}{2 \sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \sec{\left(x \right)}}$$
1
--------------------------------
_________________
/ 1
2* / 1 + ----------- *sec(x)
/ / pi\
/ sec|x - --|
\/ \ 2 /
$$\frac{1}{2 \sqrt{1 + \frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}} \sec{\left(x \right)}}$$
2/x\
1 - tan |-|
\2/
-----------------------------------------
_________________
/ /x\
/ 2*tan|-|
/ 2/x\\ / \2/
2*|1 + tan |-||* / 1 + -----------
\ \2// / 2/x\
/ 1 + tan |-|
\/ \2/
$$\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
2/x\
-1 + cot |-|
\2/
-----------------------------------------
_________________
/ /x\
/ 2*cot|-|
/ 2/x\\ / \2/
2*|1 + cot |-||* / 1 + -----------
\ \2// / 2/x\
/ 1 + cot |-|
\/ \2/
$$\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{2 \sqrt{1 + \frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
2/x pi\
1 - 2*cos |- - --|
\2 2 /
-----------------------
_________________
/ / pi\
2* / 1 + cos|x - --|
\/ \ 2 /
$$\frac{1 - 2 \cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{2 \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}}$$
1
------------------------------
____________
/ 1 /pi \
2* / 1 + ------ *csc|-- - x|
\/ csc(x) \2 /
$$\frac{1}{2 \sqrt{1 + \frac{1}{\csc{\left(x \right)}}} \csc{\left(- x + \frac{\pi}{2} \right)}}$$
/ pi\
sin|x + --|
\ 2 /
----------------
____________
2*\/ 1 + sin(x)
$$\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}}$$
2
1 - -------
2/x\
csc |-|
\2/
------------------
____________
/ 1
2* / 1 + ------
\/ csc(x)
$$\frac{1 - \frac{2}{\csc^{2}{\left(\frac{x}{2} \right)}}}{2 \sqrt{1 + \frac{1}{\csc{\left(x \right)}}}}$$
cos(x)
-----------------------
_________________
/ / pi\
2* / 1 + cos|x - --|
\/ \ 2 /
$$\frac{\cos{\left(x \right)}}{2 \sqrt{\cos{\left(x - \frac{\pi}{2} \right)} + 1}}$$
2/x\
1 - 2*sin |-|
\2/
----------------
____________
2*\/ 1 + sin(x)
$$\frac{1 - 2 \sin^{2}{\left(\frac{x}{2} \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}}$$
2/x\
8*tan |-|
\4/
1 - --------------
2
/ 2/x\\
|1 + tan |-||
\ \4//
---------------------------
_________________
/ /x\
/ 2*tan|-|
/ \2/
2* / 1 + -----------
/ 2/x\
/ 1 + tan |-|
\/ \2/
$$\frac{1 - \frac{8 \tan^{2}{\left(\frac{x}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{2}}}{2 \sqrt{1 + \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}}}$$
(1 - 8*tan(x/4)^2/(1 + tan(x/4)^2)^2)/(2*sqrt(1 + 2*tan(x/2)/(1 + tan(x/2)^2)))