Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.3 Sum and Difference Identities - 7.3 Exercises: 67

Answer

$\frac{\cos\theta-\sqrt{3}\sin\theta}{2}$

Work Step by Step

Use the addition formula for cosine, $\cos (A+B)=\cos A\cos B-\sin A\sin B$: $\cos(60^\circ+\theta)$ $=\cos 60^\circ\cos \theta-\sin 60^\circ\sin \theta$ $=\frac{1}{2}*\cos\theta-\frac{\sqrt{3}}{2}*\sin\theta$ $=\frac{\cos\theta}{2}-\frac{\sqrt{3}\sin\theta}{2}$ $=\frac{\cos\theta-\sqrt{3}\sin\theta}{2}$
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