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 952: 6


$\dfrac{\sqrt 6+\sqrt 2}{4}$

Work Step by Step

We know that $ \cos (x-y)= \cos x \cos y+ \sin x \sin y$ $\cos 15^{\circ}=\cos (45^{\circ}-30^{\circ})=\cos 45^{\circ} \cos 30^{\circ}+ \sin 45^{\circ} \sin 30^{\circ}$ $=(\dfrac{\sqrt 2}{2})(\dfrac{\sqrt 3}{2})+(\dfrac{\sqrt 2}{2}) (\dfrac{1}{2})$ $=\dfrac{\sqrt 6+\sqrt 2}{4}$
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