Algebra and Trigonometry 10th Edition

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

Chapter 7 - 7.4 - Sum and Difference Equations - 7.4 Exercises - Page 539: 73


$x=0, \dfrac{\pi}{3}, \pi, \dfrac{5\pi}{ 3}$

Work Step by Step

We have $\tan x +\pi =\dfrac{\tan x+\tan \pi}{1-\tan x \tan \pi} =\tan x$ $2 \sin x +\pi =2 (\sin x \cos \pi +\cos x \sin \pi) =2(-\sin x)$ After simplifying, we get $\tan x -2 \sin x =0$ or, $ \dfrac{\sin x}{\cos x} =2 \sin x$ or, $\sin x(2 \cos x -1)=0$ When $\sin x=0 \implies x=0, \pi$ and when $2 \cos x -1=0 \implies x= \dfrac{\pi}{3}, \dfrac{5\pi}{ 3}$ Thus, we have: $x=0, \dfrac{\pi}{3}, \pi, \dfrac{5\pi}{ 3}$
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