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: 11

Answer

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

Work Step by Step

$\cos 75=\cos \left( 45+30\right) =\cos 45\cos 30-\sin {45}\sin {30}=\dfrac {\sqrt {2}}{2}\times \dfrac {\sqrt {3}}{2}-\dfrac {\sqrt {2}}{2}\times \dfrac {1}{2}=\dfrac {\sqrt {2}}{2}\left( \sqrt {3}-1\right) $
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