If $A + B + C = {270^o},$ then $\cos \,2A + \cos 2B + \cos 2C + 4\sin A\,\sin B\,\sin C = $
$0$
$1$
$2$
$3$
$\frac{{\sec \,8\theta - 1}}{{\sec \,4\theta - 1}}$ is equal to
${\rm{cosec }}A - 2\cot 2A\cos A = $
Let $\frac{\pi}{2} < x < \pi$ be such that $\cot x=\frac{-5}{\sqrt{11}}$. Then $\left(\sin \frac{11 x}{2}\right)(\sin 6 x-\cos 6 x)+\left(\cos \frac{11 x}{2}\right)(\sin 6 x+\cos 6 x)$ is equal to
If $\cos A = \cos B\,\,\cos C$and $A + B + C = \pi ,$ then the value of $\cot \,B\,\cot \,C$ is
The value of $\sin 600^\circ \cos 330^\circ + \cos 120^\circ \sin 150^\circ $ is