Algebra and Trigonometry 10th Edition

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

Chapter 7 - Review Exercises - Page 553: 61


$x=\frac{\pi}{4}$ or $x=\frac{7\pi}{4}$

Work Step by Step

$sin(x+\frac{\pi}{4})-sin(x-\frac{\pi}{4})=1$ $sin~x~cos\frac{\pi}{4}+cos~x~sin\frac{\pi}{4}-(sin~x~cos\frac{\pi}{4}-cos~x~sin\frac{\pi}{4})=1$ $2~cos~x~sin\frac{\pi}{4}=1$ $2~cos~x~\frac{\sqrt 2}{2}=1$ $cos~x=\frac{1}{\sqrt 2}=\frac{\sqrt 2}{2}$ $x=\frac{\pi}{4}$ or $x=\frac{7\pi}{4}$
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