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: 70


$ x=\dfrac{2\pi}{3}, \dfrac{4\pi}{3}$

Work Step by Step

We have $ \cos (x +\pi) -\cos x -1=-1-2 \cos x=0$ After simplifying, we get $ \cos x \cos \pi -\sin x \sin \pi -\cos x -1=-1-2 \cos x=0$ or, $-\cos x -\cos x -1=-1-2 \cos x$ or, $-1=2 \cos x$ or, $\cos x=\dfrac{-1}{2}$ This yields: $ x=\dfrac{2\pi}{3}, \dfrac{4\pi}{3}$
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