The value of $\frac{\sin ^{3} A+\cos ^{3} A}{\sin A+\cos A}+\frac{\cos ^{3} A-\sin ^{3} A}{\cos A-\sin A}$ is

The value of $\sin^2 \frac{\pi}{8} + \sin^2 \frac{3\pi}{8} + \sin^2 \frac{5\pi}{8} + \sin^2 \frac{7\pi}{8}$ is

If $x \cos \theta = y \cos \left( \theta + \frac{2\pi}{3} \right) = z \cos \left( \theta + \frac{4\pi}{3} \right)$,then the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ is equal to

$\cos^2 48^\circ - \sin^2 12^\circ = $

If $\sec \theta + \tan \theta = m$ $(m > 1)$,then the value of $\sin \theta$ is $(0^{\circ} < \theta < 90^{\circ})$.

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 $m$)