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: 7


(a) $-\frac{\sqrt 6-\sqrt 2}{4}$ (b) $\frac{\sqrt 2+1}{2}$

Work Step by Step

$cos(u+v)=cos~u~cos~v-sin~u~sin~v$ (a) $cos(\frac{\pi}{4}+\frac{\pi}{3})=cos~\frac{\pi}{4}~cos~\frac{\pi}{3}-sin~\frac{\pi}{4}~sin~\frac{\pi}{3}=\frac{\sqrt 2}{2}~\frac{1}{2}-\frac{\sqrt 2}{2}~\frac{\sqrt 3}{2}=\frac{\sqrt 2}{4}-\frac{\sqrt 6}{4}=\frac{\sqrt 2-\sqrt 6}{4}=-\frac{\sqrt 6-\sqrt 2}{4}$ (b) $cos~\frac{\pi}{4}+cos~\frac{\pi}{3}=\frac{\sqrt 2}{2}+\frac{1}{2}=\frac{\sqrt 2+1}{2}$
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