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