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: 74


$x=0, \dfrac{\pi}{2},\dfrac{3 \pi}{2}$

Work Step by Step

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