Question

If $x=\text{CiS}\theta$, then find the value of $(x^6+\frac{1}{x^6})$.

Answer 1

It is given that,

$x=CiS\theta =\cos \theta +i\sin \theta =e^{i\theta }$

$x^6+\frac{1}{x^6}=e^{6i\theta }+\frac{1}{e^{6i\theta }}$

$⟹e^{6i\theta }+e^{-6i\theta }$

$⟹\cos 6\theta +i\sin 6\theta +\cos (-6\theta )+i\sin (-6\theta )$

$⟹\cos 6\theta +i\sin 6\theta +\cos 6\theta -i\sin 6\theta$

$⟹2\cos 6\theta$