Neha Tyagi and Amit Rastogi Solutions for Chapter: Introduction to Trigonometry and its Applications, Exercise 3: Exercise

Find the angle of elevation of the Sun when the shadow of a pole $h \mathrm{m}$ high is $\sqrt{3} h \mathrm{m}$ long.

If $\sqrt{3} \tan \theta =1,$then find the value of ${\sin }^2 \theta -{\cos }^2 \theta .$

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

If $2 {\sin }^2\theta -{\cos }^2\theta =2,$ then find the value of $\theta .$

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.

Show that ${\tan }^4 \theta +{\tan }^2 \theta ={\sec }^4 \theta -{\sec }^2 \theta .$