Let $S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^2 x}+9^{\tan ^2 x}=10\right\}$ and $\beta=\sum_{x \in S} \tan ^2\left(\frac{x}{3}\right)$, then $\frac{1}{6}(\beta-14)^2$ is equal to
$32$
$8$
$64$
$16$
The number of solution of the equation $2\cos ({e^x}) = {5^x} + {5^{ - x}}$, are
The number of solutions of the equation $4 \sin ^2 x-4$ $\cos ^3 \mathrm{x}+9-4 \cos \mathrm{x}=0 ; \mathrm{x} \in[-2 \pi, 2 \pi]$ is :
Find the solution of $\sin x=-\frac{\sqrt{3}}{2}$
The number of distinct solutions of $\sec \theta \,\, + \,\,\tan \theta \, = \,\sqrt 3 \,,\,0\,\, \leqslant \,\,\theta \,\, \leqslant \,\,2\pi$
The value of $\theta $ satisfying the given equation $\cos \theta + \sqrt 3 \sin \theta = 2,$ is