$\tan 5x - \tan 3x - \tan 2x$ is equal to

The value of $\cos^2 \frac{\pi}{12} + \cos^2 \frac{\pi}{4} + \cos^2 \frac{5\pi}{12}$ is

The sum of all values of $\theta \in (0, \frac{\pi}{2})$ satisfying $\sin^2 2\theta + \cos^4 2\theta = \frac{3}{4}$ is

$A$ ladder is placed along a wall such that its upper end is touching the top of the wall. The foot of the ladder is $10 \, ft$ away from the wall and the ladder makes an angle of $60^{\circ}$ with the ground. When a man starts climbing on it,it slips and now the ladder makes an angle of $30^{\circ}$ with the ground. How much did the ladder slip down from the top of the wall? (in $ft$)

The value of $\sin^{2} \theta + \sin^{2}(\theta + 60^{\circ}) + \sin^{2}(\theta - 60^{\circ}) =$

If $\cot 20^{\circ} = p$,then $\frac{\tan 160^{\circ} - \tan 110^{\circ}}{1 + \tan 160^{\circ} \tan 110^{\circ}} =$