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

If $A, B, C$ are angles of a triangle,then $\sin 2A + \sin 2B - \sin 2C$ is equal to

$3\,\left[ {{{\sin }^4}\,\left( {\frac{{3\pi }}{2} - \alpha } \right) + {{\sin }^4}\,(3\pi + \alpha )} \right] - 2\,\left[ {{{\sin }^6}\,\left( {\frac{\pi }{2} + \alpha } \right) + {{\sin }^6}(5\pi - \alpha )} \right] = $

$\sin \left( \frac{\pi}{10} \right) \sin \left( \frac{3\pi}{10} \right) = $

If $A + B + C = 180^\circ$,then $\sum \tan \frac{A}{2} \tan \frac{B}{2} = $

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 $m$)