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

Answer

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

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.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.