A ladder 15 m long just reaches the top of a vertical wall. If the ladders makes an angle of $60°$ with the wall, then find the height of the wall.

Simplify $\left(1+{\tan }^2 \theta \right) \left(1-\sin \theta \right) \left(1+ \sin \theta \right)$.

Show that $\frac{{\cos }^2\left(45°+\theta \right)+{\cos }^2\left(45°-\theta \right)}{\tan \left(60°+\theta \right) \tan \left(30°-\theta \right)}=1$

An observer 1.5 m tall is 20.5 m away from a tower  22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Prove that $\sqrt{{\sec }^2 \theta +{\mathrm{cosec}}^2\theta }=\tan \theta +\cot \theta$