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: 35


$\sin 2x=2\sin x\cos x$

Work Step by Step

We are trying to use $\sin(x+y)=\sin x\cos y+\cos x\sin y$ to prove $\sin 2x=2\sin x\cos x$. Start with the left side of what we're trying to prove: $\sin 2x$ Write $2x$ as $x+x$ and use the Addition Formula: $=\sin(x+x)$ $=\sin x\cos x+\cos x\sin x$ $=\sin x\cos x+\sin x\cos x$ $=2\sin x\cos x$ Since this equals the right side, the identity has been proven.
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