Sr Examen
¿Cómo vas a descomponer esta sin2x/(28(cos^2x-sin^2x)) expresión en fracciones?
Solución
Ha introducido
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sin(2*x) ---------------------- / 2 2 \ 28*\cos (x) - sin (x)/
$$\frac{\sin{\left(2 x \right)}}{28 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)}$$
sin(2*x)/((28*(cos(x)^2 - sin(x)^2)))
Simplificación general
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tan(2*x) -------- 28
$$\frac{\tan{\left(2 x \right)}}{28}$$
tan(2*x)/28
Respuesta numérica
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sin(2*x)/(28.0*cos(x)^2 - 28.0*sin(x)^2)
sin(2*x)/(28.0*cos(x)^2 - 28.0*sin(x)^2)
Denominador racional
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sin(2*x)
-------------------------
2 2
- 28*sin (x) + 28*cos (x)
$$\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}}$$
sin(2*x)/(-28*sin(x)^2 + 28*cos(x)^2)
Combinatoria
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sin(2*x) --------------------------------------- 28*(-sin(x) + cos(x))*(cos(x) + sin(x))
$$\frac{\sin{\left(2 x \right)}}{28 \left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)}$$
sin(2*x)/(28*(-sin(x) + cos(x))*(cos(x) + sin(x)))
Unión de expresiones racionales
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sin(2*x)
-------------------------
2 2
- 28*sin (x) + 28*cos (x)
$$\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}}$$
sin(2*x)/(-28*sin(x)^2 + 28*cos(x)^2)
Denominador común
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sin(2*x)
-------------------------
2 2
- 28*sin (x) + 28*cos (x)
$$\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}}$$
sin(2*x)/(-28*sin(x)^2 + 28*cos(x)^2)
Compilar la expresión
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sin(2*x)
-------------------------
2 2
- 28*sin (x) + 28*cos (x)
$$\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}}$$
sin(2*x)/(-28*sin(x)^2 + 28*cos(x)^2)
Potencias
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sin(2*x)
-------------------------
2 2
- 28*sin (x) + 28*cos (x)
$$\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}}$$
/ -2*I*x 2*I*x\
-I*\- e + e /
--------------------------------------------
/ 2\
| 2 / I*x -I*x\ |
| / -I*x I*x\ |e e | |
2*|7*\- e + e / + 28*|---- + -----| |
\ \ 2 2 / /
$$- \frac{i \left(e^{2 i x} - e^{- 2 i x}\right)}{2 \left(28 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{2} + 7 \left(e^{i x} - e^{- i x}\right)^{2}\right)}$$
-i*(-exp(-2*i*x) + exp(2*i*x))/(2*(7*(-exp(-i*x) + exp(i*x))^2 + 28*(exp(i*x)/2 + exp(-i*x)/2)^2))
Parte trigonométrica
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sin(2*x)
------------------------------
2 2/ pi\
- 28*sin (x) + 28*sin |x + --|
\ 2 /
$$\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \sin^{2}{\left(x + \frac{\pi}{2} \right)}}$$
sin(2*x)
-------------------------
2 2
- 28*sin (x) + 28*cos (x)
$$\frac{\sin{\left(2 x \right)}}{- 28 \sin^{2}{\left(x \right)} + 28 \cos^{2}{\left(x \right)}}$$
1 ---------------------------------------- / 28 28 \ / pi\ |- ------------ + -------|*sec|2*x - --| | 2/ pi\ 2 | \ 2 / | sec |x - --| sec (x)| \ \ 2 / /
$$\frac{1}{\left(- \frac{28}{\sec^{2}{\left(x - \frac{\pi}{2} \right)}} + \frac{28}{\sec^{2}{\left(x \right)}}\right) \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
/ pi\ cos|2*x - --| \ 2 / ------------- 28*cos(2*x)
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{28 \cos{\left(2 x \right)}}$$
1 ------------------------------ / 28 28 \ |- ------- + -------|*csc(2*x) | 2 2 | \ csc (x) sec (x)/
$$\frac{1}{\left(\frac{28}{\sec^{2}{\left(x \right)}} - \frac{28}{\csc^{2}{\left(x \right)}}\right) \csc{\left(2 x \right)}}$$
1 ----------- 28*cot(2*x)
$$\frac{1}{28 \cot{\left(2 x \right)}}$$
tan(2*x) -------- 28
$$\frac{\tan{\left(2 x \right)}}{28}$$
1 ----------------------------------- / 28 28 \ |- ------- + ------------|*csc(2*x) | 2 2/pi \| | csc (x) csc |-- - x|| \ \2 //
$$\frac{1}{\left(\frac{28}{\csc^{2}{\left(- x + \frac{\pi}{2} \right)}} - \frac{28}{\csc^{2}{\left(x \right)}}\right) \csc{\left(2 x \right)}}$$
2 sin (2*x) ----------- 14*sin(4*x)
$$\frac{\sin^{2}{\left(2 x \right)}}{14 \sin{\left(4 x \right)}}$$
2*tan(x)
----------------------------------------------------
/ 2\
| 2/x\ / 2/x\\ |
| 112*tan |-| 28*|1 - tan |-|| |
/ 2 \ | \2/ \ \2// |
\1 + tan (x)/*|- -------------- + -----------------|
| 2 2 |
| / 2/x\\ / 2/x\\ |
| |1 + tan |-|| |1 + tan |-|| |
\ \ \2// \ \2// /
$$\frac{2 \tan{\left(x \right)}}{\left(\frac{28 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - \frac{112 \tan^{2}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}$$
sec(2*x)
----------------
/ pi\
28*sec|2*x - --|
\ 2 /
$$\frac{\sec{\left(2 x \right)}}{28 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$
/ pi\
cos|2*x - --|
\ 2 /
------------------------------
2/ pi\ 2
- 28*cos |x - --| + 28*cos (x)
\ 2 /
$$\frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{28 \cos^{2}{\left(x \right)} - 28 \cos^{2}{\left(x - \frac{\pi}{2} \right)}}$$
2*cot(x)
-----------------------------------------------------
/ 2\
| 2/x\ / 2/x\\ |
| 112*cot |-| 28*|-1 + cot |-|| |
/ 2 \ | \2/ \ \2// |
\1 + cot (x)/*|- -------------- + ------------------|
| 2 2 |
| / 2/x\\ / 2/x\\ |
| |1 + cot |-|| |1 + cot |-|| |
\ \ \2// \ \2// /
$$\frac{2 \cot{\left(x \right)}}{\left(\frac{28 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}} - \frac{112 \cot^{2}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}$$
/pi \ csc|-- - 2*x| \2 / ------------- 28*csc(2*x)
$$\frac{\csc{\left(- 2 x + \frac{\pi}{2} \right)}}{28 \csc{\left(2 x \right)}}$$
csc(pi/2 - 2*x)/(28*csc(2*x))