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: 69

Answer

$\frac{\sqrt{2}-1}{4}$

Work Step by Step

Use the second Product-to-Sum Formula, $\cos u\sin v=\frac{1}{2}[\sin(u+v)-\sin(u-v)]$. $\cos37.5^\circ\sin7.5^\circ$ $=\frac{1}{2}[\sin(37.5^\circ+7.5^\circ)-\sin(37.5^\circ-7.5^\circ)]$ $=\frac{1}{2}(\sin 45^\circ-\sin 30^\circ)$ $=\frac{1}{2}(\frac{\sqrt{2}}{2}-\frac{1}{2})$ $=\frac{1}{2}(\frac{\sqrt{2}-1}{2})$ $=\frac{\sqrt{2}-1}{4}$
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