Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 487: 33



Work Step by Step

Recall that: $\cos(\alpha-\beta)=\cos(\alpha)\cos(\beta)+\sin(\alpha)\sin(\beta)$ Hence, $\cos(\frac{\pi}{12})\cos(\frac{5\pi}{12})+\sin(\frac{\pi}{12})\sin(\frac{5\pi}{12})=\cos\left(\frac{\pi}{12}-\frac{5\pi}{12}\right)=\cos(-\frac{\pi}{3})=\frac{1}{2}$
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