$\sqrt {\frac{{1 - \sin A}}{{1 + \sin A}}} = $

What is the simplified value of $\left[\frac{\left(\sec ^{3} x-\tan ^{3} x\right)}{(\sec x-\tan x)}\right]-2 \tan ^{2} x-\sec x \tan x ?$

If $\theta$ is eliminated from the equations $x = a \cos(\theta - \alpha)$ and $y = b \cos(\theta - \beta)$,then $\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{2xy}{ab} \cos(\alpha - \beta)$ is equal to

From an aeroplane flying vertically over a straight horizontal road,the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be $30^{\circ}$ and $60^{\circ}$. Find the height of the aeroplane above the road in miles.

The value of $\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \tan 89^{\circ}$ is

If $1+\cos^{2} \theta = 3 \sin \theta \cos \theta$,then the integral value of $\cot \theta$ is $(0 < \theta < \frac{\pi}{2})$.