Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.7 Apply Double-Angle and Half-Angle Formulas - 14.7 Exercises - Skill Practice - Page 960: 48


All the three formulas are equivalent.

Work Step by Step

We know that $\cos 2x=\cos^2 x-\sin^2 x$ ...(1) Here, we find two equations obtained form the aboive equation (1). 1) $\cos 2x=1-2 \sin^2 x \implies \cos 2x=\sin^2 x+\cos^2 x-2 \sin^2 x$ and $\cos 2x=1-2 \sin^2 x \implies \cos 2x=\cos^2 x- \sin^2 x$ 2) $\cos 2x=2 \cos^2 x -1 \implies \cos 2x=2 \cos^2 x-(\sin^2 x+cos^2 x)$ and $\cos 2x=\cos^2 x- \sin^2 x$ Hence, it has been verified that all the three formulas are equivalent.
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