Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.5 - More on Identities - 1.5 Problem Set - Page 46: 49

Answer

$\cos^{2}\theta$

Work Step by Step

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