If $\sin x + {\sin ^2}x = 1,$ then ${\cos ^8}x + 2{\cos ^6}x + {\cos ^4}x = $
$0$
$-1$
$2$
$1$
If $\sin \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1,$ then $\theta $ lies in which quadrant
Find the value of the trigonometric function $\sin \left(-\frac{11 \pi}{3}\right)$
The angle subtended at the centre of a circle of radius $3$ metres by an arc of length $1$ metre is equal to
Prove that $\frac{\cos (\pi+x) \cos (-x)}{\sin (\pi-x) \cos \left(\frac{\pi}{2}+x\right)}=\cot ^{2} x$