The value of $\sin 600^\circ \cos 330^\circ + \cos 120^\circ \sin 150^\circ $ is
$-1$
$1$
$\frac{1}{{\sqrt 2 }}$
$\frac{{\sqrt 3 }}{2}$
If ${\cos ^6}\alpha + {\sin ^6}\alpha + K\,{\sin ^2}2\alpha = 1,$ then $K =$
$\left( {1 + \cos \frac{\pi }{8}} \right)\,\left( {1 + \cos \frac{{3\pi }}{8}} \right)\,\left( {1 + \cos \frac{{5\pi }}{8}} \right)\,\left( {1 + \cos \frac{{7\pi }}{8}} \right) = $
Number of values of $ x \in \left[ {0,2\pi } \right]$ satisfying the equation $cotx - cosx = 1 - cotx. cosx$
Prove that: $\cos 4 x=1-8 \sin ^{2} x \cos ^{2} x$
Prove that $\frac{\sin x-\sin 3 x}{\sin ^{2} x-\cos ^{2} x}=2 \sin x$