If $12{\cot ^2}\theta - 31\,{\rm{cosec }}\theta + {\rm{32}} = {\rm{0}}$, then the value of $\sin \theta $ is
$\frac{3}{5}$ or $1$
$\frac{{2}}{3}$ or $\frac{{ - 2}}{3}$
$\frac{4}{5}$ or $\frac{3}{4}$
$ \pm \frac{1}{2}$
If $cosx + secx =\, -2$, then for a $+ve$ integer $n$, $cos^n x + sec^n x$ is
The number of solution of the equation,$\sum\limits_{r = 1}^5 {\cos (r\,x)} $ $= 0$ lying in $(0, \pi)$ is :
The sum of all values of $x$ in $[0,2 \pi]$, for which $\sin x+\sin 2 x+\sin 3 x+\sin 4 x=0$, is equal to:
The number of values of $\alpha $ in $[0, 2\pi]$ for which $2\,{\sin ^3}\,\alpha - 7\,{\sin ^2}\,\alpha + 7\,\sin \,\alpha = 2$ , is
The general value $\theta $ is obtained from the equation $\cos 2\theta = \sin \alpha ,$ is