Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.5 - Multiple-Angle and Product-to-Sum Formulas - 7.5 Exercises - Page 548: 9


$x=2n\pi$, where $n$ is an integer. $x=\frac{2\pi}{3}+2n\pi$, where $n$ is an integer. $x=\frac{4\pi}{3}+2n\pi$, where $n$ is an integer.

Work Step by Step

$cos~2x-cos~x=0$ $cos^2x-sin^2x-cos~x=0$ $cos^2x+cos^2x-1-cos~x=0$ $2~cos^2x-cos~x-1=0$ $cos~x=1$ and $cos~x=-\frac{1}{2}$ The solutions in [0,2π) are: $x=0$ $x=\frac{2\pi}{3}$ $x=\frac{4\pi}{3}$ General solution: $x=0+2n\pi=2n\pi$ $x=\frac{2\pi}{3}+2n\pi$ $x=\frac{4\pi}{3}+2n\pi$ where $n$ is an integer.
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