Number of roots of the equation ${\cos ^2}x + \frac{{\sqrt 3 + 1}}{2}\sin x - \frac{{\sqrt 3 }}{4} - 1 = 0$ which lie in the interval $[-\pi,\pi ]$ is
$2$
$4$
$6$
$8$
Find the solution of $\sin x=-\frac{\sqrt{3}}{2}$
If $\tan 2\theta \tan \theta = 1$, then the general value of $\theta $ is
If $12{\cot ^2}\theta - 31\,{\rm{cosec }}\theta + {\rm{32}} = {\rm{0}}$, then the value of $\sin \theta $ is
If$\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0$, where $0 < \theta < {180^o}$, then $\theta =$
Number of solution $(s)$ of equation $cosec\, \theta -cot \,\theta = 1$ in $[0,2 \pi]$ is-