Algebra and Trigonometry 10th Edition

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

Chapter 7 - Review Exercises - Page 552: 44


$x=\frac{\pi}{4}+n\pi$ $x=arctan~\frac{1}{2}+n\pi$ where $n$ is an integer.

Work Step by Step

$2~tan^2x-3~tan~x=-1$ $2~tan^2x-2~tan~x-tan~x+1=0$ $2~tan~x(tan~x-1)-(tan~x-1)=0$ $(tan~x-1)(2~tan~x-1)=0$ $tan~x=1$ or $tan~x=\frac{1}{2}$ $tan~x=1$ $x=\frac{\pi}{4}$ $tan~x=\frac{1}{2}$ $x=arctan~\frac{1}{2}$ The period of $tan~x$ is $\pi$. The general solutions are: $x=\frac{\pi}{4}+n\pi$ $x=arctan~\frac{1}{2}+n\pi$ where $n$ is an integer.
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