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