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 Formulas - 7.4 Exercises - Page 538: 36


$cos~\frac{\pi}{16}~cos~\frac{3\pi}{16}-sin~\frac{\pi}{16}~sin~\frac{3\pi}{16}=\frac{\sqrt 2}{2}$

Work Step by Step

$cos(u+v)=cos~u~cos~v-sin~u~sin~v$ $cos~\frac{\pi}{16}~cos~\frac{3\pi}{16}-sin~\frac{\pi}{16}~sin~\frac{3\pi}{16}=cos(\frac{\pi}{16}+\frac{3\pi}{16})=cos~\frac{4\pi}{16}=cos~\frac{\pi}{4}=\frac{\sqrt 2}{2}$
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