# Chapter 1 - Section 1.5 - More on Identities - 1.5 Problem Set - Page 46: 51

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

#### Work Step by Step

Given expression is- $(1-\tan\theta) (1+\tan\theta)$ = $1 + \tan\theta -\tan\theta - \tan^{2}\theta$ ( By FOIL method) = $1- \tan^{2}\theta$ ( Recall first Pythagorean identity) ALTERNATE METHOD- Recall that $(A-B) (A+B) = A^{2} - B^{2}$ Therefore $(1-\tan\theta) (1+\tan\theta)$ = $1^{2} - \tan^{2}\theta$ = $1 - \tan^{2}\theta$

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