Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.6 Trigonometric Equations - 7.6 Exercises: 37

Answer

$\{0^{o}, 45^{o},135^{o}, 180^{o},225^{o},315^{o}\}$

Work Step by Step

.. subtract $ 2\tan\theta$ from both sides ... $\sec^{2}\theta\tan\theta-2\tan\theta=0$ $\tan\theta(\sec^{2}\theta-2)=0$ ... zero factor principle ... 1. $\quad \tan\theta =0 \ \Rightarrow\ \theta=0^{o}, 180^{o}$ or 2.$\quad \sec^{2}\theta=2 \ \Rightarrow\ \sec\theta=\pm\sqrt{2} \ \Rightarrow\ $ $\displaystyle \ \Rightarrow\ \cos\theta=\pm\frac{1}{\sqrt{2}}=\frac{\pm\sqrt{2}}{2}$ $\ \Rightarrow\ \theta=45^{o},135^{o},225^{o},315^{o}$ Solution set = $\{0^{o}, 45^{o},135^{o}, 180^{o},225^{o},315^{o}\}$
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