Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.3 Sum and Difference Identities - 7.3 Exercises: 69

Answer

$\dfrac {\sqrt {2}}{2}\left( \sin x-\cos x\right) $

Work Step by Step

$\cos \left( \dfrac {3\pi }{4}-x\right) =\cos \dfrac {3\pi }{4}\cos x+\sin \dfrac {3\pi }{4}\sin x=-\dfrac {\sqrt {2}}{2}\cos x+\dfrac {\sqrt {2}}{2}\sin x=\dfrac {\sqrt {2}}{2}\left( \sin x-\cos x\right) $
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