The value of $\cos \frac{\pi}{2^2} \cdot \cos \frac{\pi}{2^3} \cdot \dots \cdot \cos \frac{\pi}{2^{10}} \cdot \sin \frac{\pi}{2^{10}}$ is

If $\sin A = \frac{3}{5}$,$\tan B = \frac{1}{2}$,and $\frac{\pi}{2} < A < \pi < B < \frac{3\pi}{2}$,then the value of $8 \tan A - \sqrt{5} \sec B$ is:

The value of $\cos \frac{\pi}{10} \cos \frac{2\pi}{10} \cos \frac{4\pi}{10} \cos \frac{8\pi}{10} \cos \frac{16\pi}{10}$ is:

If $2\cos\theta + \sin\theta = 1$,then the value of $4\cos\theta + 3\sin\theta$ is equal to

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

To an observer on the ground,the angle of elevation of the top of a tower is $30^{\circ}$. If the height of the tower is $100 \ m$,find the distance between the top of the tower and the point of observation (in meters).