The value of $\sin 600^\circ \cos 330^\circ + \cos 120^\circ \sin 150^\circ $ is

Prove that: $\cos 4 x=1-8 \sin ^{2} x \cos ^{2} x$

The expression $[1 - sin (3\pi - \alpha ) + cos (3\pi + \alpha )]$ $\left[ {1\,\, - \,\,\sin \,\left( {\frac{{3\,\pi }}{2}\,\, - \,\,\alpha } \right)\,\, + \,\,\cos \,\left( {\frac{{5\,\pi }}{2}\,\, - \,\,\alpha } \right)} \right]$ when simplified reduces to :

$2{\cos ^2}\theta - 2{\sin ^2}\theta = 1$, then $\theta  =$ .......$^o$

$1 + \cos \,{56^o} + \cos \,{58^o} - \cos {66^o} = $

$96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$ is equal to$......$.