Sr Examen
¿Cómo vas a descomponer esta sin(2*a)/(cos(2*a)+sin(2*a)) expresión en fracciones?
Solución
Ha introducido
[src]
sin(2*a) ------------------- cos(2*a) + sin(2*a)
$$\frac{\sin{\left(2 a \right)}}{\sin{\left(2 a \right)} + \cos{\left(2 a \right)}}$$
sin(2*a)/(cos(2*a) + sin(2*a))
Simplificación general
[src]
___
\/ 2 *sin(2*a)
---------------
/ pi\
2*sin|2*a + --|
\ 4 /
$$\frac{\sqrt{2} \sin{\left(2 a \right)}}{2 \sin{\left(2 a + \frac{\pi}{4} \right)}}$$
sqrt(2)*sin(2*a)/(2*sin(2*a + pi/4))
Potencias
[src]
/ -2*I*a 2*I*a\
-I*\- e + e /
---------------------------------------------
/ -2*I*a 2*I*a / -2*I*a 2*I*a\\
|e e I*\- e + e /|
2*|------- + ------ - ----------------------|
\ 2 2 2 /
$$- \frac{i \left(e^{2 i a} - e^{- 2 i a}\right)}{2 \left(- \frac{i \left(e^{2 i a} - e^{- 2 i a}\right)}{2} + \frac{e^{2 i a}}{2} + \frac{e^{- 2 i a}}{2}\right)}$$
-i*(-exp(-2*i*a) + exp(2*i*a))/(2*(exp(-2*i*a)/2 + exp(2*i*a)/2 - i*(-exp(-2*i*a) + exp(2*i*a))/2))
Parte trigonométrica
[src]
___
\/ 2 *sin(2*a)
---------------
/ pi\
2*sin|2*a + --|
\ 4 /
$$\frac{\sqrt{2} \sin{\left(2 a \right)}}{2 \sin{\left(2 a + \frac{\pi}{4} \right)}}$$
/ pi\
cos|2*a - --|
\ 2 /
------------------------
/ pi\
cos(2*a) + cos|2*a - --|
\ 2 /
$$\frac{\cos{\left(2 a - \frac{\pi}{2} \right)}}{\cos{\left(2 a \right)} + \cos{\left(2 a - \frac{\pi}{2} \right)}}$$
1 ---------------------------------------- / 1 1 \ / pi\ |-------- + -------------|*sec|2*a - --| |sec(2*a) / pi\| \ 2 / | sec|2*a - --|| \ \ 2 //
$$\frac{1}{\left(\frac{1}{\sec{\left(2 a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(2 a \right)}}\right) \sec{\left(2 a - \frac{\pi}{2} \right)}}$$
sin(2*a)
------------------------
/pi \
sin(2*a) + sin|-- + 2*a|
\2 /
$$\frac{\sin{\left(2 a \right)}}{\sin{\left(2 a \right)} + \sin{\left(2 a + \frac{\pi}{2} \right)}}$$
2*tan(a)
-----------------------------------------
/ 2 \
/ 2 \ |1 - tan (a) 2*tan(a) |
\1 + tan (a)/*|----------- + -----------|
| 2 2 |
\1 + tan (a) 1 + tan (a)/
$$\frac{2 \tan{\left(a \right)}}{\left(\frac{1 - \tan^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1} + \frac{2 \tan{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1}\right) \left(\tan^{2}{\left(a \right)} + 1\right)}$$
___ 2 / pi\
\/ 2 *sin (a)*cot(a)*tan|a + --|
\ 8 /
--------------------------------
2/ pi\
2*sin |a + --|
\ 8 /
$$\frac{\sqrt{2} \sin^{2}{\left(a \right)} \tan{\left(a + \frac{\pi}{8} \right)} \cot{\left(a \right)}}{2 \sin^{2}{\left(a + \frac{\pi}{8} \right)}}$$
___ / pi\
\/ 2 *csc|2*a + --|*sin(2*a)
\ 4 /
----------------------------
2
$$\frac{\sqrt{2} \sin{\left(2 a \right)} \csc{\left(2 a + \frac{\pi}{4} \right)}}{2}$$
1 ----------------------------------- / 1 1 \ |-------- + -------------|*csc(2*a) |csc(2*a) /pi \| | csc|-- - 2*a|| \ \2 //
$$\frac{1}{\left(\frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(2 a \right)}}\right) \csc{\left(2 a \right)}}$$
1 ------------------------------ / 1 1 \ |-------- + --------|*csc(2*a) \csc(2*a) sec(2*a)/
$$\frac{1}{\left(\frac{1}{\sec{\left(2 a \right)}} + \frac{1}{\csc{\left(2 a \right)}}\right) \csc{\left(2 a \right)}}$$
___ / pi\
\/ 2 *sec|2*a - --|*sin(2*a)
\ 4 /
----------------------------
2
$$\frac{\sqrt{2} \sin{\left(2 a \right)} \sec{\left(2 a - \frac{\pi}{4} \right)}}{2}$$
___ / 2/ pi\\
\/ 2 *|1 + cot |a + --||*cot(a)
\ \ 8 //
-------------------------------
/ 2 \ / pi\
2*\1 + cot (a)/*cot|a + --|
\ 8 /
$$\frac{\sqrt{2} \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right) \cot{\left(a \right)}}{2 \left(\cot^{2}{\left(a \right)} + 1\right) \cot{\left(a + \frac{\pi}{8} \right)}}$$
___
\/ 2 *sin(2*a)
---------------
/ pi\
2*cos|2*a - --|
\ 4 /
$$\frac{\sqrt{2} \sin{\left(2 a \right)}}{2 \cos{\left(2 a - \frac{\pi}{4} \right)}}$$
___ 2 / 2/ pi\\
\/ 2 *cos (a)*|1 + tan |a + --||*tan(a)
\ \ 8 //
---------------------------------------
/ pi\
2*tan|a + --|
\ 8 /
$$\frac{\sqrt{2} \left(\tan^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(a \right)} \tan{\left(a \right)}}{2 \tan{\left(a + \frac{\pi}{8} \right)}}$$
2*cot(a)
------------------------------------------
/ 2 \
/ 2 \ |-1 + cot (a) 2*cot(a) |
\1 + cot (a)/*|------------ + -----------|
| 2 2 |
\1 + cot (a) 1 + cot (a)/
$$\frac{2 \cot{\left(a \right)}}{\left(\frac{\cot^{2}{\left(a \right)} - 1}{\cot^{2}{\left(a \right)} + 1} + \frac{2 \cot{\left(a \right)}}{\cot^{2}{\left(a \right)} + 1}\right) \left(\cot^{2}{\left(a \right)} + 1\right)}$$
___ / 2/ pi\\
\/ 2 *|1 + tan |a + --||*tan(a)
\ \ 8 //
-------------------------------
/ 2 \ / pi\
2*\1 + tan (a)/*tan|a + --|
\ 8 /
$$\frac{\sqrt{2} \left(\tan^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right) \tan{\left(a \right)}}{2 \left(\tan^{2}{\left(a \right)} + 1\right) \tan{\left(a + \frac{\pi}{8} \right)}}$$
___ / pi\
\/ 2 *csc|2*a + --|
\ 4 /
-------------------
2*csc(2*a)
$$\frac{\sqrt{2} \csc{\left(2 a + \frac{\pi}{4} \right)}}{2 \csc{\left(2 a \right)}}$$
___ / pi\
\/ 2 *cos|2*a - --|
\ 2 /
-------------------
/ pi\
2*cos|2*a - --|
\ 4 /
$$\frac{\sqrt{2} \cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos{\left(2 a - \frac{\pi}{4} \right)}}$$
___ / pi\
\/ 2 *sec|2*a - --|
\ 4 /
-------------------
/ pi\
2*sec|2*a - --|
\ 2 /
$$\frac{\sqrt{2} \sec{\left(2 a - \frac{\pi}{4} \right)}}{2 \sec{\left(2 a - \frac{\pi}{2} \right)}}$$
sqrt(2)*sec(2*a - pi/4)/(2*sec(2*a - pi/2))