If $7 \sin^{2} \theta + 3 \cos^{2} \theta = 4$,then the value of $\tan \theta$ is (where $\theta$ is acute).

The minimum value of $\cos 2\theta + \cos \theta$ for real values of $\theta$ is

The equation $\sec^2 \theta = \frac{4xy}{(x + y)^2}$ is only possible when

The value of $\tan 20^{\circ} + \tan 40^{\circ} + \tan 60^{\circ} + \cdots + \tan 180^{\circ}$ is

The angle of elevation of the top of a vertical tower situated perpendicularly on a plane is observed as $60^{\circ}$ from a point $P$ on the same plane. From another point $Q$,$10\, m$ vertically above the point $P$,the angle of depression of the foot of the tower is $30^{\circ}$. The height of the tower is (in $m$)

The value of $\sin 780^{\circ} \sin 480^{\circ} + \cos 240^{\circ} \cos 300^{\circ} = $