If $2{\sin ^2}\theta = 3\cos \theta ,$ where $0 \le \theta \le 2\pi $, then $\theta = $
$\frac{\pi }{6},\frac{{7\pi }}{6}$
$\frac{\pi }{3},\frac{{5\pi }}{3}$
$\frac{\pi }{3},\frac{{7\pi }}{3}$
None of these
If $\sec x\cos 5x + 1 = 0$, where $0 < x < 2\pi $, then $x =$
The general solution of $\frac{{\tan \,2x\, - \,\tan \,x}}{{1\, + \,\tan \,x\,\tan \,2x}}\, = \,1$ is
The general value of $\theta $satisfying the equation $2{\sin ^2}\theta - 3\sin \theta - 2 = 0$ is
If $1 + \sin x + {\sin ^2}x + .....$ to $\infty = 4 + 2\sqrt 3 ,\,0 < x < \pi ,$ then
The solution of the equation $cos^2\theta\, +\, sin\theta\, + 1\, =\, 0$ lies in the interval