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: 73


$\cos^2 5x-\sin^2 5x=\cos 10x$

Work Step by Step

Start from the right side, write $10x$ as $2*5x$, and use the double-angle formula $\cos 2s=\cos^2 s-\sin^2 s$ with $s=5x$: $\cos 10x$ =$\cos (2*5x)$ $=\cos^2 5x-\sin^2 5x$ Since this equals the left side, the identity is proven.
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