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-
$0$
$1$
$2$
$3$
The general value of $\theta $ satisfying the equation $\tan \theta + \tan \left( {\frac{\pi }{2} - \theta } \right) = 2$, is
The solution of $3\tan (A - {15^o}) = \tan (A + {15^o})$ is
If $\tan \theta + \tan 2\theta + \tan 3\theta = \tan \theta \tan 2\theta \tan 3\theta $, then the general value of $\theta $ is
The angles $\alpha, \beta, \gamma$ of a triangle satisfy the equations $2 \sin \alpha+3 \cos \beta=3 \sqrt{2}$ and $3 \sin \beta+2 \cos \alpha=1$. Then, angle $\gamma$ equals
The number of solutions to $\sin x=\frac{6}{x}$ with $0 \leq x \leq 12 \pi$ is