Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.6 Apply Sum and Difference Formulas - 14.6 Exercises - Skill Practice - Page 953: 38


$x= \dfrac{3 \pi}{4}, \dfrac{ 7 \pi}{4}$

Work Step by Step

Use formula: $\sin (x+y)= \sin x \cos y+\cos x \sin y\\ \cos (x+y)= \cos x \cos y- \sin x \sin y$ Here, we have $\cos x \cos \pi -\sin x \sin \pi +\sin x \cos \pi +\cos x \sin \pi=0$ This gives: $-\cos x- \sin x=0$ or, $\tan x=-1$ Hence, the solution for $x$ is: $x= \dfrac{3 \pi}{4}, \dfrac{ 7 \pi}{4}$
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