The value of $6(\sin^6 \theta + \cos^6 \theta) - 9(\sin^4 \theta + \cos^4 \theta) + 4$ is

If $\tan A = n \tan B$ and $\sin A = m \sin B ,$ then the value of $\cos ^{2} A$ is

The value of the expression $2(\sin^6 \theta + \cos^6 \theta) - 3(\sin^4 \theta + \cos^4 \theta) + 1$ is

The value of $\cos y \cos \left( \frac{\pi}{2} - x \right) - \cos \left( \frac{\pi}{2} - y \right) \cos x + \sin y \cos \left( \frac{\pi}{2} - x \right) + \cos x \sin \left( \frac{\pi}{2} - y \right)$ is zero,if

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).

For $A = 133^\circ$,$2\cos \frac{A}{2}$ is equal to