Sr Examen
¿Cómo vas a descomponer esta cos(90*pi/(360+x)) expresión en fracciones?
Solución
Ha introducido
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/ 90*pi \ cos|-------| \360 + x/
$$\cos{\left(\frac{90 \pi}{x + 360} \right)}$$
cos((90*pi)/(360 + x))
Parte trigonométrica
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1 ----------------- /pi 90*pi \ csc|-- - -------| \2 360 + x/
$$\frac{1}{\csc{\left(\frac{\pi}{2} - \frac{90 \pi}{x + 360} \right)}}$$
2/ 45*pi \
1 - tan |-------|
\360 + x/
-----------------
2/ 45*pi \
1 + tan |-------|
\360 + x/
$$\frac{1 - \tan^{2}{\left(\frac{45 \pi}{x + 360} \right)}}{\tan^{2}{\left(\frac{45 \pi}{x + 360} \right)} + 1}$$
1 ------------ / 90*pi \ sec|-------| \360 + x/
$$\frac{1}{\sec{\left(\frac{90 \pi}{x + 360} \right)}}$$
2/ 45*pi \
-1 + cot |-------|
\360 + x/
------------------
2/ 45*pi \
1 + cot |-------|
\360 + x/
$$\frac{\cot^{2}{\left(\frac{45 \pi}{x + 360} \right)} - 1}{\cot^{2}{\left(\frac{45 \pi}{x + 360} \right)} + 1}$$
/pi 90*pi \ sin|-- + -------| \2 360 + x/
$$\sin{\left(\frac{\pi}{2} + \frac{90 \pi}{x + 360} \right)}$$
sin(pi/2 + 90*pi/(360 + x))
Potencias
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-90*pi*I 90*pi*I
-------- -------
360 + x 360 + x
e e
--------- + --------
2 2
$$\frac{e^{\frac{90 i \pi}{x + 360}}}{2} + \frac{e^{- \frac{90 i \pi}{x + 360}}}{2}$$
exp(-90*pi*i/(360 + x))/2 + exp(90*pi*i/(360 + x))/2