Chapter 13.6, Problem 5WE

To determine

To find: The simplification for given term.

Answer to Problem 5WE

The simplification is ${\cos }^2\theta$ .

Explanation of Solution

Given:

The given term is,

  $\left(1-\sin \theta \right)\left(1+\sin \theta \right)$

Calculation:

The term is simplified as,

  $\begin{array}{c}\left(1-\sin \theta \right)\left(1+\sin \theta \right)=1-{\sin }^2\theta \\ ={\cos }^2\theta \end{array}$

Therefore, the simplification is ${\cos }^2\theta$ .