Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.3 - Solving Trigonometric Equations - 7.3 Exercises - Page 531: 60


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

Work Step by Step

Use: $-tan~x=tan~x-2~tan~x$ $tan^2x-tan~x-2=0~~$ $tan^2x+tan~x-2~tan~x-2=0$ $tan~x(tan~x+1)-2(tan~x+1)=0$ $(tan~x-2)(tan~x+1)=0$ $tan~x-2=0$ $tan~x=2$ $x=arctan~2$ $tan~x+1=0$ $tan~x=-1$ $x=arctan(-1)=-\frac{\pi}{4}$ The period of $tan~x$ is $\pi$. So, add multiples of $\pi$ to each solution to find the general solution: $x=arctan~2+n\pi$ and $x=-\frac{\pi}{4}+n\pi$, where $n$ is an integer.
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