$\cot 5^o - \tan 5^o - 2 \tan 10^o - 4 \tan 20^o - 8 \cot 40^o$ is equal to

$A$ 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 $ft$)

If $m$ and $M$ are the minimum and the maximum values of $4 + \frac{1}{2} \sin^2 2x - 2 \cos^4 x$ for $x \in R$,then $M - m$ is equal to

If $\sin \theta = \frac{3}{5},$ then the value of $\frac{\tan \theta + \cos \theta}{\cot \theta + \operatorname{cosec} \theta}$ is equal to

The value of $\tan 56^{\circ} - \tan 11^{\circ} - \tan 56^{\circ} \tan 11^{\circ}$ is

The value of $\frac{\tan x}{\tan 3x}$,whenever defined,never lies between: