Sr Examen
¿Cómo vas a descomponer esta sin(x)/(9*cos(x)) expresión en fracciones?
Solución
Ha introducido
[src]
sin(x) -------- 9*cos(x)
$$\frac{\sin{\left(x \right)}}{9 \cos{\left(x \right)}}$$
sin(x)/((9*cos(x)))
Parte trigonométrica
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/ pi\ cos|x - --| \ 2 / ----------- 9*cos(x)
$$\frac{\cos{\left(x - \frac{\pi}{2} \right)}}{9 \cos{\left(x \right)}}$$
tan(x) ------ 9
$$\frac{\tan{\left(x \right)}}{9}$$
1 -------- 9*cot(x)
$$\frac{1}{9 \cot{\left(x \right)}}$$
sec(x) -------- 9*csc(x)
$$\frac{\sec{\left(x \right)}}{9 \csc{\left(x \right)}}$$
/x\
2*tan|-|
\2/
---------------
/ 2/x\\
9*|1 - tan |-||
\ \2//
$$\frac{2 \tan{\left(\frac{x}{2} \right)}}{9 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)}$$
/x\
2*cot|-|
\2/
----------------
/ 2/x\\
9*|-1 + cot |-||
\ \2//
$$\frac{2 \cot{\left(\frac{x}{2} \right)}}{9 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}$$
2 2*sin (x) ---------- 9*sin(2*x)
$$\frac{2 \sin^{2}{\left(x \right)}}{9 \sin{\left(2 x \right)}}$$
sin(x)
-------------
/ pi\
9*sin|x + --|
\ 2 /
$$\frac{\sin{\left(x \right)}}{9 \sin{\left(x + \frac{\pi}{2} \right)}}$$
sec(x)
-------------
/ pi\
9*sec|x - --|
\ 2 /
$$\frac{\sec{\left(x \right)}}{9 \sec{\left(x - \frac{\pi}{2} \right)}}$$
/pi \ csc|-- - x| \2 / ----------- 9*csc(x)
$$\frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{9 \csc{\left(x \right)}}$$
csc(pi/2 - x)/(9*csc(x))
Potencias
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/ -I*x I*x\ -I*\- e + e / -------------------- / I*x -I*x\ |9*e 9*e | 2*|------ + -------| \ 2 2 /
$$- \frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(\frac{9 e^{i x}}{2} + \frac{9 e^{- i x}}{2}\right)}$$
-i*(-exp(-i*x) + exp(i*x))/(2*(9*exp(i*x)/2 + 9*exp(-i*x)/2))