Precalculus (6th Edition)

Published by Pearson

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises: 23

Answer

$\cos 30=\dfrac {\sqrt {3}}{2}$

Work Step by Step

$\cos ^{2}\alpha =\cos ^{2}\alpha -\sin ^{2}\alpha =1-2\sin ^{2}\alpha \Rightarrow 1-2\sin ^{2}15=\cos \left( 2\times 15\right) =\cos 30=\dfrac {\sqrt {3}}{2}$

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