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: 32

Answer

a. $\cos \theta$ b. $\sin \theta$

Work Step by Step

a. Use the formula $\cos 2x=\cos^2 x-\sin^2 x$ with $x=\frac{\theta}{2}$. Then $\cos^2 \frac{\theta}{2}-\sin^2\frac{\theta}{2}=\cos(2*\frac{\theta}{2})=\cos \theta$. b. Use the formula $\sin 2x=2\sin x\cos x$ with $x=\frac{\theta}{2}$. Then $2\sin \frac{\theta}{2}\cos \frac{\theta}{2}=\sin(2*\frac{\theta}{2})=\sin \theta$.
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