The solution set of the system of inequations
$2{\sin }^{2}x-3\sin x+1\le 0$ and $x^2+x-12\le 0$ has

If $\frac{\sin A}{\sin B}=\frac{\sqrt{3}}{2}$ and $\frac{\cos A}{\cos B}=\frac{\sqrt{5}}{2}, 0<A, B<\frac{\pi }{2}$, then $\tan A+\tan B$ is equal to

For $-\frac{\pi }{2}<\theta <\frac{\pi }{2}$, $\frac{\sin \theta +\sin 2\theta }{1+\cos \theta +\cos 2\theta }$ lies in the interval

The general solution of the equation ${\tan }^2\alpha +2\sqrt{3}\tan \alpha =1$ is given by