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