Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(x)/(a*sqrt(1-cos(x)^2/(a^2)))
¿Cómo vas a descomponer esta sin(x)/(a*sqrt(1-cos(x)^2/(a^2))) expresión en fracciones?
Solución
Ha introducido
[src]
sin(x)
---------------------
_____________
/ 2
/ cos (x)
a* / 1 - -------
/ 2
\/ a
$$\frac{\sin{\left(x \right)}}{a \sqrt{1 - \frac{\cos^{2}{\left(x \right)}}{a^{2}}}}$$
sin(x)/((a*sqrt(1 - cos(x)^2/a^2)))
Potencias
[src]
/ -I*x I*x\
-I*\- e + e /
----------------------------------
_____________________
/ 2
/ / I*x -I*x\
/ |e e |
/ |---- + -----|
/ \ 2 2 /
2*a* / 1 - ---------------
/ 2
\/ a
$$- \frac{i \left(e^{i x} - e^{- i x}\right)}{2 a \sqrt{1 - \frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2}}{a^{2}}}}$$
-i*(-exp(-i*x) + exp(i*x))/(2*a*sqrt(1 - (exp(i*x)/2 + exp(-i*x)/2)^2/a^2))
Unión de expresiones racionales
[src]
sin(x)
----------------------
______________
/ 2 2
/ a - cos (x)
a* / ------------
/ 2
\/ a
$$\frac{\sin{\left(x \right)}}{a \sqrt{\frac{a^{2} - \cos^{2}{\left(x \right)}}{a^{2}}}}$$
sin(x)/(a*sqrt((a^2 - cos(x)^2)/a^2))
Parte trigonométrica
[src]
/x\
2*tan|-|
\2/
-------------------------------------------------
_______________________
/ 2
/ / 2/x\\
/ |1 - tan |-||
/ 2/x\\ / \ \2//
a*|1 + tan |-||* / 1 - -----------------
\ \2// / 2
/ 2 / 2/x\\
/ a *|1 + tan |-||
\/ \ \2//
$$\frac{2 \tan{\left(\frac{x}{2} \right)}}{a \sqrt{1 - \frac{\left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{a^{2} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}} \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
/x\
2*cot|-|
\2/
-------------------------------------------------
_______________________
/ 2
/ / 2/x\\
/ |-1 + cot |-||
/ 2/x\\ / \ \2//
a*|1 + cot |-||* / 1 - -----------------
\ \2// / 2
/ 2 / 2/x\\
/ a *|1 + cot |-||
\/ \ \2//
$$\frac{2 \cot{\left(\frac{x}{2} \right)}}{a \sqrt{1 - \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{a^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$
___ /x\
2*\/ 2 *cot|-|
\2/
-------------------------------------------------
___________________________
/ 2
/ 2/x\\ / 1 -1 + cot (x)
a*|1 + cot |-||* / 2 - -- - ----------------
\ \2// / 2 2 / 2 \
\/ a a *\1 + cot (x)/
$$\frac{2 \sqrt{2} \cot{\left(\frac{x}{2} \right)}}{a \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \sqrt{2 - \frac{\cot^{2}{\left(x \right)} - 1}{a^{2} \left(\cot^{2}{\left(x \right)} + 1\right)} - \frac{1}{a^{2}}}}$$
___
\/ 2 *sin(x)
--------------------------
___________________
/ 1 cos(2*x)
a* / 2 - -- - --------
/ 2 2
\/ a a
$$\frac{\sqrt{2} \sin{\left(x \right)}}{a \sqrt{2 - \frac{\cos{\left(2 x \right)}}{a^{2}} - \frac{1}{a^{2}}}}$$
/ pi\
cos|x - --|
\ 2 /
---------------------
_____________
/ 2
/ cos (x)
a* / 1 - -------
/ 2
\/ a
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{a \sqrt{1 - \frac{\cos^{2}{\left(x \right)}}{a^{2}}}}$$
1
------------------------------------
_____________________
/ 1
a* / 1 - --------------- *csc(x)
/ 2 2/pi \
/ a *csc |-- - x|
\/ \2 /
$$\frac{1}{a \sqrt{1 - \frac{1}{a^{2} \csc^{2}{\left(- x + \frac{\pi}{2} \right)}}} \csc{\left(x \right)}}$$
1
-----------------------------------
________________
/ 1 / pi\
a* / 1 - ---------- *sec|x - --|
/ 2 2 \ 2 /
\/ a *sec (x)
$$\frac{1}{a \sqrt{1 - \frac{1}{a^{2} \sec^{2}{\left(x \right)}}} \sec{\left(x - \frac{\pi}{2} \right)}}$$
___
\/ 2
------------------------------------------
___________________________
/ 1 1
a* / 2 - -- - ---------------- *csc(x)
/ 2 2 /pi \
/ a a *csc|-- - 2*x|
\/ \2 /
$$\frac{\sqrt{2}}{a \sqrt{2 - \frac{1}{a^{2}} - \frac{1}{a^{2} \csc{\left(- 2 x + \frac{\pi}{2} \right)}}} \csc{\left(x \right)}}$$
___
\/ 2 *sin(x)
---------------------------------
________________________
/ /pi \
/ sin|-- + 2*x|
/ 1 \2 /
a* / 2 - -- - -------------
/ 2 2
\/ a a
$$\frac{\sqrt{2} \sin{\left(x \right)}}{a \sqrt{2 - \frac{\sin{\left(2 x + \frac{\pi}{2} \right)}}{a^{2}} - \frac{1}{a^{2}}}}$$
___ / pi\
\/ 2 *cos|x - --|
\ 2 /
--------------------------
___________________
/ 1 cos(2*x)
a* / 2 - -- - --------
/ 2 2
\/ a a
$$\frac{\sqrt{2} \cos{\left(x - \frac{\pi}{2} \right)}}{a \sqrt{2 - \frac{\cos{\left(2 x \right)}}{a^{2}} - \frac{1}{a^{2}}}}$$
___ /x\
2*\/ 2 *tan|-|
\2/
-------------------------------------------------
___________________________
/ 2
/ 2/x\\ / 1 1 - tan (x)
a*|1 + tan |-||* / 2 - -- - ----------------
\ \2// / 2 2 / 2 \
\/ a a *\1 + tan (x)/
$$\frac{2 \sqrt{2} \tan{\left(\frac{x}{2} \right)}}{a \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \sqrt{2 - \frac{1 - \tan^{2}{\left(x \right)}}{a^{2} \left(\tan^{2}{\left(x \right)} + 1\right)} - \frac{1}{a^{2}}}}$$
1
------------------------------
________________
/ 1
a* / 1 - ---------- *csc(x)
/ 2 2
\/ a *sec (x)
$$\frac{1}{a \sqrt{1 - \frac{1}{a^{2} \sec^{2}{\left(x \right)}}} \csc{\left(x \right)}}$$
___
\/ 2
-----------------------------------------
______________________
/ 1 1 / pi\
a* / 2 - -- - ----------- *sec|x - --|
/ 2 2 \ 2 /
\/ a a *sec(2*x)
$$\frac{\sqrt{2}}{a \sqrt{2 - \frac{1}{a^{2}} - \frac{1}{a^{2} \sec{\left(2 x \right)}}} \sec{\left(x - \frac{\pi}{2} \right)}}$$
sin(x)
---------------------------
__________________
/ 2/ pi\
/ sin |x + --|
/ \ 2 /
a* / 1 - ------------
/ 2
\/ a
$$\frac{\sin{\left(x \right)}}{a \sqrt{1 - \frac{\sin^{2}{\left(x + \frac{\pi}{2} \right)}}{a^{2}}}}$$
sin(x)/(a*sqrt(1 - sin(x + pi/2)^2/a^2))
Combinatoria
[src]
sin(x)
-----------------------------------
_____________________________
/ / cos(x)\ / cos(x)\
a* / -|1 + ------|*|-1 + ------|
\/ \ a / \ a /
$$\frac{\sin{\left(x \right)}}{a \sqrt{- \left(-1 + \frac{\cos{\left(x \right)}}{a}\right) \left(1 + \frac{\cos{\left(x \right)}}{a}\right)}}$$
sin(x)/(a*sqrt(-(1 + cos(x)/a)*(-1 + cos(x)/a)))