$\left( \frac{\sin 2A}{1 + \cos 2A} \right) \left( \frac{\cos A}{1 + \cos A} \right) = $

If $\cos A = m \cos B,$ then

$A$ 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 $\sec ^{2} 12^{\circ}-\frac{1}{\tan ^{2} 78^{\circ}}$ is

The value of $x$ for the maximum value of $(\sqrt{3} \sin x + \cos x)$ is .....$^o$

If $x + y + z = 180^o,$ then $\cos 2x + \cos 2y - \cos 2z$ is equal to