Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sqrt(3)*cos(x)/(3*sqrt(1-2*sin(x)^2/3))
¿Cómo vas a descomponer esta sqrt(3)*cos(x)/(3*sqrt(1-2*sin(x)^2/3)) expresión en fracciones?
Solución
Ha introducido
[src]
___
\/ 3 *cos(x)
----------------------
_______________
/ 2
/ 2*sin (x)
3* / 1 - ---------
\/ 3
$$\frac{\sqrt{3} \cos{\left(x \right)}}{3 \sqrt{- \frac{2 \sin^{2}{\left(x \right)}}{3} + 1}}$$
(sqrt(3)*cos(x))/((3*sqrt(1 - 2*sin(x)^2/3)))
Simplificación general
[src]
cos(x) ---------------- ______________ \/ 2 + cos(2*x)
$$\frac{\cos{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)} + 2}}$$
cos(x)/sqrt(2 + cos(2*x))
Potencias
[src]
/ I*x -I*x\
___ |e e |
\/ 3 *|---- + -----|
\ 2 2 /
-------------------------------
_______________________
/ 2
/ / -I*x I*x\
/ \- e + e /
3* / 1 + -----------------
\/ 6
$$\frac{\sqrt{3} \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)}{3 \sqrt{\frac{\left(e^{i x} - e^{- i x}\right)^{2}}{6} + 1}}$$
___
\/ 3 *cos(x)
----------------------
_______________
/ 2
/ 2*sin (x)
3* / 1 - ---------
\/ 3
$$\frac{\sqrt{3} \cos{\left(x \right)}}{3 \sqrt{1 - \frac{2 \sin^{2}{\left(x \right)}}{3}}}$$
sqrt(3)*cos(x)/(3*sqrt(1 - 2*sin(x)^2/3))
Denominador racional
[src]
_______________
/ 2
-\/ 3 - 2*sin (x) *cos(x)
---------------------------
2
-3 + 2*sin (x)
$$- \frac{\sqrt{3 - 2 \sin^{2}{\left(x \right)}} \cos{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 3}$$
-sqrt(3 - 2*sin(x)^2)*cos(x)/(-3 + 2*sin(x)^2)
Denominador común
[src]
cos(x) ------------------ _______________ / 2 \/ 3 - 2*sin (x)
$$\frac{\cos{\left(x \right)}}{\sqrt{3 - 2 \sin^{2}{\left(x \right)}}}$$
cos(x)/sqrt(3 - 2*sin(x)^2)
Unión de expresiones racionales
[src]
cos(x) ------------------ _______________ / 2 \/ 3 - 2*sin (x)
$$\frac{\cos{\left(x \right)}}{\sqrt{3 - 2 \sin^{2}{\left(x \right)}}}$$
cos(x)/sqrt(3 - 2*sin(x)^2)
Combinatoria
[src]
cos(x) ------------------ _______________ / 2 \/ 3 - 2*sin (x)
$$\frac{\cos{\left(x \right)}}{\sqrt{3 - 2 \sin^{2}{\left(x \right)}}}$$
cos(x)/sqrt(3 - 2*sin(x)^2)
Respuesta numérica
[src]
0.577350269189626*(1.0 - 0.666666666666667*sin(x)^2)^(-0.5)*cos(x)
0.577350269189626*(1.0 - 0.666666666666667*sin(x)^2)^(-0.5)*cos(x)
Compilar la expresión
[src]
___
\/ 3 *cos(x)
----------------------
_______________
/ 2
/ 2*sin (x)
3* / 1 - ---------
\/ 3
$$\frac{\sqrt{3} \cos{\left(x \right)}}{3 \sqrt{1 - \frac{2 \sin^{2}{\left(x \right)}}{3}}}$$
sqrt(3)*cos(x)/(3*sqrt(1 - 2*sin(x)^2/3))
Parte trigonométrica
[src]
2/x\
-1 + cot |-|
\2/
--------------------------------------
__________________
/ 2
/ 2/x\\ / -1 + cot (x)
|1 + cot |-||* / 2 + ------------
\ \2// / 2
\/ 1 + cot (x)
$$\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\sqrt{\frac{\cot^{2}{\left(x \right)} - 1}{\cot^{2}{\left(x \right)} + 1} + 2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
___
\/ 3 *cos(x)
----------------------
_______________
/ 2
/ 2*sin (x)
3* / 1 - ---------
\/ 3
$$\frac{\sqrt{3} \cos{\left(x \right)}}{3 \sqrt{1 - \frac{2 \sin^{2}{\left(x \right)}}{3}}}$$
___
\/ 3
-----------------------------
_______________
/ 2
3* / 1 - --------- *sec(x)
/ 2
\/ 3*csc (x)
$$\frac{\sqrt{3}}{3 \sqrt{1 - \frac{2}{3 \csc^{2}{\left(x \right)}}} \sec{\left(x \right)}}$$
___
\/ 3 *cos(x)
----------------------------
____________________
/ 2/ pi\
/ 2*cos |x - --|
/ \ 2 /
3* / 1 - --------------
\/ 3
$$\frac{\sqrt{3} \cos{\left(x \right)}}{3 \sqrt{1 - \frac{2 \cos^{2}{\left(x - \frac{\pi}{2} \right)}}{3}}}$$
cos(x) ---------------- ______________ \/ 2 + cos(2*x)
$$\frac{\cos{\left(x \right)}}{\sqrt{\cos{\left(2 x \right)} + 2}}$$
___ / 2/x\\
\/ 3 *|-1 + cot |-||
\ \2//
-----------------------------------------------
______________________
/ 2/x\
/ 8*cot |-|
/ 2/x\\ / \2/
3*|1 + cot |-||* / 1 - ----------------
\ \2// / 2
/ / 2/x\\
/ 3*|1 + cot |-||
\/ \ \2//
$$\frac{\sqrt{3} \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{3 \sqrt{1 - \frac{8 \cot^{2}{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/ pi\
sin|x + --|
\ 2 /
-----------------------
___________________
/ /pi \
/ 2 + sin|-- + 2*x|
\/ \2 /
$$\frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\sqrt{\sin{\left(2 x + \frac{\pi}{2} \right)} + 2}}$$
___ / pi\
\/ 3 *sin|x + --|
\ 2 /
----------------------
_______________
/ 2
/ 2*sin (x)
3* / 1 - ---------
\/ 3
$$\frac{\sqrt{3} \sin{\left(x + \frac{\pi}{2} \right)}}{3 \sqrt{1 - \frac{2 \sin^{2}{\left(x \right)}}{3}}}$$
1
-------------------------
______________
/ 1
/ 2 + -------- *sec(x)
\/ sec(2*x)
$$\frac{1}{\sqrt{2 + \frac{1}{\sec{\left(2 x \right)}}} \sec{\left(x \right)}}$$
___
\/ 3
-----------------------------------
____________________
/ 2
3* / 1 - -------------- *sec(x)
/ 2/ pi\
/ 3*sec |x - --|
\/ \ 2 /
$$\frac{\sqrt{3}}{3 \sqrt{1 - \frac{2}{3 \sec^{2}{\left(x - \frac{\pi}{2} \right)}}} \sec{\left(x \right)}}$$
___
\/ 3
----------------------------------
_______________
/ 2 /pi \
3* / 1 - --------- *csc|-- - x|
/ 2 \2 /
\/ 3*csc (x)
$$\frac{\sqrt{3}}{3 \sqrt{1 - \frac{2}{3 \csc^{2}{\left(x \right)}}} \csc{\left(- x + \frac{\pi}{2} \right)}}$$
2/x\
1 - tan |-|
\2/
-------------------------------------
_________________
/ 2
/ 2/x\\ / 1 - tan (x)
|1 + tan |-||* / 2 + -----------
\ \2// / 2
\/ 1 + tan (x)
$$\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\sqrt{\frac{1 - \tan^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1} + 2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
___ / 2/x\\
\/ 3 *|1 - tan |-||
\ \2//
-----------------------------------------------
______________________
/ 2/x\
/ 8*tan |-|
/ 2/x\\ / \2/
3*|1 + tan |-||* / 1 - ----------------
\ \2// / 2
/ / 2/x\\
/ 3*|1 + tan |-||
\/ \ \2//
$$\frac{\sqrt{3} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}{3 \sqrt{1 - \frac{8 \tan^{2}{\left(\frac{x}{2} \right)}}{3 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
1
-------------------------------------
___________________
/ 1 /pi \
/ 2 + ------------- *csc|-- - x|
/ /pi \ \2 /
/ csc|-- - 2*x|
\/ \2 /
$$\frac{1}{\sqrt{2 + \frac{1}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \csc{\left(- x + \frac{\pi}{2} \right)}}$$
1/(sqrt(2 + 1/csc(pi/2 - 2*x))*csc(pi/2 - x))