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 - Page 679: 13

Answer

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

Work Step by Step

$\cos \left( -105\right) =\cos \left( -60-45\right) =\cos (-60)\cos (-45)+\sin (-60)\sin (-45)=\dfrac {1}{2}\times \dfrac {\sqrt {2}}{2}+\left( -\dfrac {\sqrt {3}}{2}\right) \times \left( -\dfrac {\sqrt {2}}{2}\right) =\dfrac {\sqrt {2}}{4}\left( 1+\sqrt {3}\right) $
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