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: 53

Answer

$1 - 2\sin\theta\cos\theta $

Work Step by Step

Given expression- $ (\sin\theta-\cos\theta)^{2} $ = $ (\sin\theta-\cos\theta) (\sin\theta-\cos\theta) $ ( recall $a^{2} = a\times a$) = $ \cos^{2}\theta -\cos\theta\sin\theta -\sin\theta\cos\theta + \sin^{2}\theta$ (By FOIL method) = $ \cos^{2}\theta + \sin^{2}\theta - 2\sin\theta\cos\theta $ = $1 - 2\sin\theta\cos\theta $ ( From first Pythagorean identity $ \cos^{2}\theta + \sin^{2}\theta$ = 1 )
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