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