Chapter 14.2, Problem 2CYP

To determine

To Find : Which option is equal to ${\tan }^2\theta ({\cot }^2\theta -{\cos }^2\theta )$

Answer to Problem 2CYP

Option H

Explanation of Solution

Given information :

We know that, the given value is ${\tan }^2\theta ({\cot }^2\theta -{\cos }^2\theta )$

Proof :

The given equation is

  $\begin{array}{l}{\tan }^2\theta ({\cot }^2\theta -{\cos }^2\theta )\\ ={\tan }^2\theta \times {\cot }^2\theta -{\tan }^2\theta \times {\cos }^2\theta \\ =\frac{1}{{\cot }^2\theta }\times {\cot }^2\theta -\frac{{\sin }^2\theta }{{\cos }^2\theta }\times {\cos }^2\theta \\ =1-{\sin }^2\theta \\ ={\cos }^2\theta \end{array}$