Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 71



Work Step by Step

Use the first Sum-to-Product Formula, $\cos x-\cos y=-2\sin \frac{x+y}{2}\sin\frac{x-y}{2}$. $\cos 255^\circ-\cos 195^\circ$ $=-2\sin \frac{255^\circ+195^\circ}{2}\sin \frac{255^\circ-195^\circ}{2}$ $=-2\sin \frac{450^\circ}{2}\sin\frac{60^\circ}{2}$ $=-2\sin 225^\circ\sin 30^\circ$ $=-2\times(-\frac{\sqrt{2}}{2})\times\frac{1}{2}$ $=\frac{\sqrt{2}}{2}$
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