Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.3 Sum and Difference Identities - 7.3 Exercises: 18

Answer

$\dfrac {\sqrt {2}}{4}\left( 1-\sqrt {3}\right) $

Work Step by Step

$\cos \left( -\dfrac {7\pi }{12}\right) =\cos \left( \left( -\dfrac {\pi }{3}\right) +\left( -\dfrac {\pi }{4}\right) \right) =\cos \left( -\dfrac {\pi }{3}\right) \cos \left( -\dfrac {\pi }{4}\right) -\sin \left( -\dfrac {\pi }{3}\right) \sin \left( -\dfrac {\pi }{4}\right)=\dfrac {1}{2}\times \dfrac {\sqrt {2}}{2}-\dfrac {\sqrt {3}}{2}\times \dfrac {\sqrt {2}}{2}=\dfrac {\sqrt {2}}{4}\left( 1-\sqrt {3}\right) $
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