If $x\sin 45^\circ {\cos ^2}60^\circ = \frac{{{{\tan }^2}60^\circ {\rm{cosec}}30^\circ }}{{\sec 45^\circ {{\cot }^2}30^\circ }},$ then $x = $

Which of the following relations is possible

If $\tan \theta = \frac{{20}}{{21}},$ cos$\theta$ will be

Prove that: $(\cos x+\cos y)^{2}+(\sin x-\sin y)^{2}=4 \cos ^{2} \frac{x+y}{2}$

The value of $2({\sin ^6}\theta + {\cos ^6}\theta ) - 3({\sin ^4}\theta + {\cos ^4}\theta ) + 1$ is

Find the value of $\sin \frac{31 \pi}{3}$.