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: 8


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

Work Step by Step

$sin~2x~sin~x=cos~x$ $2~sin~x~cos~x~sin~x-cos~x=0$ $cos~x~(2~sin^2x-1)=0$ $sin~x=±\frac{\sqrt 2}{2}$ or $cos~x=0$ The solutions in $[0,2\pi)$ are: $x=\frac{\pi}{4}$, $x=\frac{3\pi}{4}=\frac{\pi}{2}+\frac{\pi}{4}$, $x=\frac{5\pi}{4}=2\frac{\pi}{2}+\frac{\pi}{4}$, $x=\frac{7\pi}{4}=3\frac{\pi}{2}+\frac{\pi}{4}$, $x=\frac{\pi}{2}$ and $x=\frac{3\pi}{2}=\pi+\frac{\pi}{2}$ General solution: $x=\frac{\pi}{4}+n\frac{\pi}{2}$ and $x=\frac{\pi}{2}+n\pi$, where $n$ is an integer.
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