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: 70



Work Step by Step

Use the first Sum-to-Product Formula, $\sin x+\sin y=2\sin \frac{x+y}{2}\cos\frac{x-y}{2}$. $\sin 75^\circ+\sin 15^\circ$ $=2\sin \frac{75^\circ+15^\circ}{2}\cos \frac{75^\circ-15^\circ}{2}$ $=2\sin \frac{90^\circ}{2}\cos\frac{60^\circ}{2}$ $=2\sin 45^\circ\cos 30^\circ$ $=2\times\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}$ $=\frac{\sqrt{6}}{2}$
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