Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises: 45

Answer

$-2\sin 11.5^{o}\cdot\cos 36.5^{o}$

Work Step by Step

Sum-to-Product: $\displaystyle \sin A+\sin B=2\sin(\frac{A+B}{2})\cos(\frac{A-B}{2})$ $\sin(-A)=-\sin A$ ---------- $\displaystyle \frac{A+B}{2}=\frac{25^{o}+(-48)^{o}}{2}=-11.5^{o}$ $\displaystyle \frac{A-B}{2}=\frac{25^{o}-(-48)^{o}}{2}=36.5^{o}$ $\sin 25^{o}+\sin(-48^{o})=2\sin(-11.5^{o})\cdot\cos(36.5^{o})$ $=-2\sin 11.5^{o}\cdot\cos 36.5^{o}$
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