$\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ} = $

The angle of elevation of the top of a tower is $30^{\circ}$. On walking $100 \ m$ towards the tower,the angle of elevation of the top of the tower becomes $60^{\circ}$. Find the height of the tower (in $m$).

If $A = \sin^8 \theta + \cos^{14} \theta$,then for all real values of $\theta$:

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

If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha$ and $\beta$ are positive acute angles,then

If $\sin \theta = \frac{1}{2} \left( \sqrt{\frac{x}{y}} + \sqrt{\frac{y}{x}} \right)$,where $x, y \in R - \{0\}$. Then: