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 530: 30


$x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$

Work Step by Step

$cos~x+sin~x~tan~x=2$ $cos~x+sin~x~\frac{sin~x}{cos~x}=2$ $\frac{cos~x(cos~x)}{cos~x}+\frac{sin^2x}{cos~x}=2$ $\frac{cos^2x+sin^2x}{cos~x}=2$ $\frac{1}{cos~x}=2$ $cos~x=\frac{1}{2}$ The solutions in the interval $[0,2\pi)$ are: $x=\frac{\pi}{3}$ and $x=\frac{5\pi}{3}$
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