Sr Examen
¿Cómo vas a descomponer esta ctg(3п/2-а)/(1-tg^2a) expresión en fracciones?
Solución
Ha introducido
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/3*pi \
cot|---- - a|
\ 2 /
-------------
2
1 - tan (a)
$$\frac{\cot{\left(- a + \frac{3 \pi}{2} \right)}}{1 - \tan^{2}{\left(a \right)}}$$
cot((3*pi)/2 - a)/(1 - tan(a)^2)
Descomposición de una fracción
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-1/(2*(1 + tan(a))) - 1/(2*(-1 + tan(a)))
$$- \frac{1}{2 \left(\tan{\left(a \right)} + 1\right)} - \frac{1}{2 \left(\tan{\left(a \right)} - 1\right)}$$
1 1 - -------------- - --------------- 2*(1 + tan(a)) 2*(-1 + tan(a))
Potencias
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tan(a)
---------------------
2
/ I*a -I*a\
\- e + e /
1 + -----------------
2
/ I*a -I*a\
\e + e /
$$\frac{\tan{\left(a \right)}}{\frac{\left(- e^{i a} + e^{- i a}\right)^{2}}{\left(e^{i a} + e^{- i a}\right)^{2}} + 1}$$
tan(a)
-----------
2
1 - tan (a)
$$\frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
tan(a)/(1 - tan(a)^2)
Unión de expresiones racionales
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/-2*a + 3*pi\
cot|-----------|
\ 2 /
----------------
2
1 - tan (a)
$$\frac{\cot{\left(\frac{- 2 a + 3 \pi}{2} \right)}}{1 - \tan^{2}{\left(a \right)}}$$
cot((-2*a + 3*pi)/2)/(1 - tan(a)^2)
Combinatoria
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-tan(a) -------------------------- (1 + tan(a))*(-1 + tan(a))
$$- \frac{\tan{\left(a \right)}}{\left(\tan{\left(a \right)} - 1\right) \left(\tan{\left(a \right)} + 1\right)}$$
-tan(a)/((1 + tan(a))*(-1 + tan(a)))
Denominador común
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-tan(a)
------------
2
-1 + tan (a)
$$- \frac{\tan{\left(a \right)}}{\tan^{2}{\left(a \right)} - 1}$$
-tan(a)/(-1 + tan(a)^2)
Denominador racional
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-tan(a)
------------
2
-1 + tan (a)
$$- \frac{\tan{\left(a \right)}}{\tan^{2}{\left(a \right)} - 1}$$
-tan(a)/(-1 + tan(a)^2)
Parte trigonométrica
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1 -------------------- / 1 \ |1 - -------|*cot(a) | 2 | \ cot (a)/
$$\frac{1}{\left(1 - \frac{1}{\cot^{2}{\left(a \right)}}\right) \cot{\left(a \right)}}$$
2 sin (2*a) --------- sin(4*a)
$$\frac{\sin^{2}{\left(2 a \right)}}{\sin{\left(4 a \right)}}$$
sec(2*a)
---------------
/ pi\
2*sec|2*a - --|
\ 2 /
$$\frac{\sec{\left(2 a \right)}}{2 \sec{\left(2 a - \frac{\pi}{2} \right)}}$$
tan(a)
-----------
2
1 - tan (a)
$$\frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
1 -------------------- / 2 \ \1 - tan (a)/*cot(a)
$$\frac{1}{\left(1 - \tan^{2}{\left(a \right)}\right) \cot{\left(a \right)}}$$
/ pi\ cos|2*a - --| \ 2 / ------------- 2*cos(2*a)
$$\frac{\cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos{\left(2 a \right)}}$$
/pi \ csc|-- - 2*a| \2 / ------------- 2*csc(2*a)
$$\frac{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}{2 \csc{\left(2 a \right)}}$$
sin(2*a) ------------------------- / 4 \ | 4*sin (a)| 2 2*|1 - ---------|*cos (a) | 2 | \ sin (2*a)/
$$\frac{\sin{\left(2 a \right)}}{2 \left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \cos^{2}{\left(a \right)}}$$
sin(2*a) ------------------------------ / 4 \ | 4*sin (a)| 2/ pi\ 2*|1 - ---------|*sin |a + --| | 2 | \ 2 / \ sin (2*a)/
$$\frac{\sin{\left(2 a \right)}}{2 \left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \sin^{2}{\left(a + \frac{\pi}{2} \right)}}$$
sec(a) ------------------------------ / 2 \ | sec (a) | / pi\ |1 - ------------|*sec|a - --| | 2/ pi\| \ 2 / | sec |a - --|| \ \ 2 //
$$\frac{\sec{\left(a \right)}}{\left(- \frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(a - \frac{\pi}{2} \right)}}$$
-sin(a) ------------------------------ / 2/ pi\\ | cos |a - --|| | \ 2 /| |1 - ------------|*cos(pi - a) | 2 | \ cos (a) /
$$- \frac{\sin{\left(a \right)}}{\left(1 - \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}\right) \cos{\left(\pi - a \right)}}$$
tan(a)
-----------
1
1 - -------
2
cot (a)
$$\frac{\tan{\left(a \right)}}{1 - \frac{1}{\cot^{2}{\left(a \right)}}}$$
tan(2*a) -------- 2
$$\frac{\tan{\left(2 a \right)}}{2}$$
1 ---------- 2*cot(2*a)
$$\frac{1}{2 \cot{\left(2 a \right)}}$$
sec(a) -------------------- / 2 \ | sec (a)| |1 - -------|*csc(a) | 2 | \ csc (a)/
$$\frac{\sec{\left(a \right)}}{\left(1 - \frac{\sec^{2}{\left(a \right)}}{\csc^{2}{\left(a \right)}}\right) \csc{\left(a \right)}}$$
/pi \
csc|-- - a|
\2 /
-------------------------
/ 2/pi \\
| csc |-- - a||
| \2 /|
|1 - ------------|*csc(a)
| 2 |
\ csc (a) /
$$\frac{\csc{\left(- a + \frac{\pi}{2} \right)}}{\left(1 - \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}\right) \csc{\left(a \right)}}$$
/ pi\
cos|a - --|
\ 2 /
--------------------
/ 2 \
| sin (a)|
|1 - -------|*cos(a)
| 2 |
\ cos (a)/
$$\frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\left(- \frac{\sin^{2}{\left(a \right)}}{\cos^{2}{\left(a \right)}} + 1\right) \cos{\left(a \right)}}$$
cos(a - pi/2)/((1 - sin(a)^2/cos(a)^2)*cos(a))