$\sin 75^\circ = $

Let $E = \left( {1 - \frac{{\cos 61^\circ}}{{\cos 1^\circ}}} \right) \left( {1 - \frac{{\cos 62^\circ}}{{\cos 2^\circ}}} \right) \dots \left( {1 - \frac{{\cos 119^\circ}}{{\cos 59^\circ}}} \right)$,then $E$ is equal to:

If $5 \tan \theta = 4$,then $\frac{5 \sin \theta - 3 \cos \theta}{5 \sin \theta + 2 \cos \theta} = $

If $\sin \alpha = \frac{2pq}{p^2 + q^2}$,then $\sec \alpha - \tan \alpha = $

Let $A = \{ \theta : 2\cos^2 \theta + \sin \theta \le 2 \}$ and $B = \{ \theta : \frac{\pi}{2} \le \theta \le \frac{3\pi}{2} \}$,then $A \cap B$ is

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 $m$).