$1 - 2{\sin ^2}\left( {\frac{\pi }{4} + \theta } \right) = $

$\sin 12^\circ \sin 48^\circ \sin 54^\circ = $

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

$2\sin A{\cos ^3}A - 2{\sin ^3}A\cos A = $

If $\sin \theta  = \frac{1}{2}\left( {\sqrt {\frac{x}{y}\,}  + \,\sqrt {\frac{y}{x}} } \right)\,,\,\left( {x,y \in R\, - \{ 0\} } \right)$. Then

$\cos \frac{{2\pi }}{{15}}\cos \frac{{4\pi }}{{15}}\cos \frac{{8\pi }}{{15}}\cos \frac{{16\pi }}{{15}}  =$