Question

If $\omega$ is cube root of unity then the value of $\sin \left[\right({\omega }^{202}+{\omega }^{200})\pi -\frac{\pi }{4}]$ equals

• A. $\frac{1}{\sqrt{2}}$
• B. $-\frac{1}{\sqrt{2}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $-\frac{\sqrt{3}}{2}$

Answer 1

The correct option is A $\frac{1}{\sqrt{2}}$

${\omega }^{202}+{\omega }^{200}$
$=\omega +{\omega }^2$
$=-1$
Hence,
$sin(-\pi -\frac{\pi }{4})$
$=-sin(\pi +\frac{\pi }{4})$
$=\frac{1}{\sqrt{2}}$