Chapter 14.2, Problem 4CYU

To determine

To Verify :The given Equation ${\tan }^2\theta =\frac{1-{\cos }^2\theta }{{\cos }^2\theta }$

Explanation of Solution

Given information :

We know that, the given value is ${\tan }^2\theta =\frac{1-{\cos }^2\theta }{{\cos }^2\theta }$

Formula Used :

  ${\sec }^2\theta -1={\tan }^2\theta$

Calculation :

The given equation is

  $\begin{array}{l}R.H.S.=\frac{1-{\cos }^2\theta }{{\cos }^2\theta }\\ =\frac{1}{{\cos }^2\theta }-\frac{{\cos }^2\theta }{{\cos }^2\theta }\\ ={\sec }^2\theta -1\\ ={\tan }^2\theta \\ =L.H.S.\end{array}$