Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(2*x)/(28*cos(2*x)-sin(2*x))
¿Cómo vas a descomponer esta sin(2*x)/(28*cos(2*x)-sin(2*x)) expresión en fracciones?
Solución
Ha introducido
[src]
sin(2*x) ---------------------- 28*cos(2*x) - sin(2*x)
$$\frac{\sin{\left(2 x \right)}}{- \sin{\left(2 x \right)} + 28 \cos{\left(2 x \right)}}$$
sin(2*x)/(28*cos(2*x) - sin(2*x))
Potencias
[src]
/ -2*I*x 2*I*x\
-I*\- e + e /
---------------------------------------------------
/ / -2*I*x 2*I*x\\
| -2*I*x 2*I*x I*\- e + e /|
2*|14*e + 14*e + ----------------------|
\ 2 /
$$- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(\frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2} + 14 e^{2 i x} + 14 e^{- 2 i x}\right)}$$
-i*(-exp(-2*i*x) + exp(2*i*x))/(2*(14*exp(-2*i*x) + 14*exp(2*i*x) + i*(-exp(-2*i*x) + exp(2*i*x))/2))
Parte trigonométrica
[src]
-2*tan(x)
------------------------------------------------
/ / 2 \ \
/ 2 \ | 28*\1 - tan (x)/ 2*tan(x) |
\1 + tan (x)/*|- ---------------- + -----------|
| 2 2 |
\ 1 + tan (x) 1 + tan (x)/
$$- \frac{2 \tan{\left(x \right)}}{\left(- \frac{28 \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1} + \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}$$
/ pi\
cos|2*x - --|
\ 2 /
-----------------------------
/ pi\
- cos|2*x - --| + 28*cos(2*x)
\ 2 /
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{28 \cos{\left(2 x \right)} - \cos{\left(2 x - \frac{\pi}{2} \right)}}$$
2*cot(x)
-------------------------------------------------
/ / 2 \\
/ 2 \ | 2*cot(x) 28*\-1 + cot (x)/|
\1 + cot (x)/*|- ----------- + -----------------|
| 2 2 |
\ 1 + cot (x) 1 + cot (x) /
$$\frac{2 \cot{\left(x \right)}}{\left(\frac{28 \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1} - \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}$$
/ pi\
-cos|2*x - --|
\ 2 /
----------------------------
/ pi\
-28*cos(2*x) + cos|2*x - --|
\ 2 /
$$- \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{- 28 \cos{\left(2 x \right)} + \cos{\left(2 x - \frac{\pi}{2} \right)}}$$
1 ------------------------------------------ / 1 28 \ / pi\ |- ------------- + --------|*sec|2*x - --| | / pi\ sec(2*x)| \ 2 / | sec|2*x - --| | \ \ 2 / /
$$\frac{1}{\left(- \frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}} + \frac{28}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
-sin(2*x) ----------------------- -28*cos(2*x) + sin(2*x)
$$- \frac{\sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 28 \cos{\left(2 x \right)}}$$
-sin(2*x)
-----------------------------
/pi \
- 28*sin|-- + 2*x| + sin(2*x)
\2 /
$$- \frac{\sin{\left(2 x \right)}}{\sin{\left(2 x \right)} - 28 \sin{\left(2 x + \frac{\pi}{2} \right)}}$$
2*tan(x)
------------------------------------------------
/ / 2 \\
/ 2 \ | 2*tan(x) 28*\1 - tan (x)/|
\1 + tan (x)/*|- ----------- + ----------------|
| 2 2 |
\ 1 + tan (x) 1 + tan (x) /
$$\frac{2 \tan{\left(x \right)}}{\left(\frac{28 \left(1 - \tan^{2}{\left(x \right)}\right)}{\tan^{2}{\left(x \right)} + 1} - \frac{2 \tan{\left(x \right)}}{\tan^{2}{\left(x \right)} + 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}$$
-1 ---------------------------------------- / 1 28 \ / pi\ |------------- - --------|*sec|2*x - --| | / pi\ sec(2*x)| \ 2 / |sec|2*x - --| | \ \ 2 / /
$$- \frac{1}{\left(\frac{1}{\sec{\left(2 x - \frac{\pi}{2} \right)}} - \frac{28}{\sec{\left(2 x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
1 ------------------------------------- / 1 28 \ |- -------- + -------------|*csc(2*x) | csc(2*x) /pi \| | csc|-- - 2*x|| \ \2 //
$$\frac{1}{\left(\frac{28}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(2 x \right)}}\right) \csc{\left(2 x \right)}}$$
1 -------------------------------- / 1 28 \ |- -------- + --------|*csc(2*x) \ csc(2*x) sec(2*x)/
$$\frac{1}{\left(\frac{28}{\sec{\left(2 x \right)}} - \frac{1}{\csc{\left(2 x \right)}}\right) \csc{\left(2 x \right)}}$$
-1 ----------------------------------- / 1 28 \ |-------- - -------------|*csc(2*x) |csc(2*x) /pi \| | csc|-- - 2*x|| \ \2 //
$$- \frac{1}{\left(- \frac{28}{\csc{\left(- 2 x + \frac{\pi}{2} \right)}} + \frac{1}{\csc{\left(2 x \right)}}\right) \csc{\left(2 x \right)}}$$
-2*cot(x)
-------------------------------------------------
/ / 2 \ \
/ 2 \ | 28*\-1 + cot (x)/ 2*cot(x) |
\1 + cot (x)/*|- ----------------- + -----------|
| 2 2 |
\ 1 + cot (x) 1 + cot (x)/
$$- \frac{2 \cot{\left(x \right)}}{\left(- \frac{28 \left(\cot^{2}{\left(x \right)} - 1\right)}{\cot^{2}{\left(x \right)} + 1} + \frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}$$
sin(2*x)
----------------------------
/pi \
-sin(2*x) + 28*sin|-- + 2*x|
\2 /
$$\frac{\sin{\left(2 x \right)}}{- \sin{\left(2 x \right)} + 28 \sin{\left(2 x + \frac{\pi}{2} \right)}}$$
sin(2*x)/(-sin(2*x) + 28*sin(pi/2 + 2*x))