The smallest positive angle which satisfies the equation $2{\sin ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$, is
$\frac{{5\pi }}{6}$
$\frac{{2\pi }}{3}$
$\frac{\pi }{3}$
$\frac{\pi }{6}$
Solve $2 \cos ^{2} x+3 \sin x=0$
If both roots of quadratic equation ${x^2} + \left( {\sin \,\theta + \cos \,\theta } \right)x + \frac{3}{8} = 0$ are positive and distinct then complete set of values of $\theta $ in $\left[ {0,2\pi } \right]$ is
If $\cot (\alpha + \beta ) = 0,$ then $\sin (\alpha + 2\beta ) = $
Number of solution$(s)$ of the equation $\sin 2\theta + \cos 2\theta = - \frac{1}{2},\theta \in \left( {0,\frac{\pi }{2}} \right)$ is-
The general value $\theta $ is obtained from the equation $\cos 2\theta = \sin \alpha ,$ is