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: 40


$x=\dfrac{\pi}{3}, \dfrac{2 \pi}{3}, \dfrac{4 \pi}{3}, \dfrac{ 5\pi}{3}$

Work Step by Step

Use the identity double angle formula: $ 2 \cos^2 x-1=-2 \cos^2 x$ Then, we have $4 \cos^2 x-1 =0$ $\implies \cos^2 x=\dfrac{1}{4}$ Here, $\cos x=\dfrac{1}{2}$ and $\cos x=- \dfrac{1}{2}$ Thus, we have $x=\dfrac{\pi}{3}, \dfrac{2 \pi}{3}, \dfrac{4 \pi}{3}, \dfrac{ 5\pi}{3}$
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