Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.4 - Sum and Difference Equations - 7.4 Exercises - Page 539: 60


The identity is verified. $cos(\frac{5\pi}{4}-x)=-\frac{\sqrt 2}{2}(cos~x+sin~x)$

Work Step by Step

$cos(u-v)=cos~u~cos~v+sin~u~sin~v$ $cos(\frac{5\pi}{4}-x)=cos~\frac{5\pi}{4}~cos~x+sin~\frac{5\pi}{4}~sin~x=-\frac{\sqrt 2}{2}cos~x+(-\frac{\sqrt 2}{2})sin~x=-\frac{\sqrt 2}{2}(cos~x+sin~x)$
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