Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.5 Double-Angle Identities - 5.5 Exercises - Page 237: 37



Work Step by Step

$$X=\cos^215^\circ-\sin^215^\circ$$ - From Double-Angle Identity for cosine: $$\cos2A=\cos^2A-\sin^2A$$ So if you replace the above identity with $A=15^\circ$ as in $X$, we get $$X=\cos(2\times15^\circ)$$ $$X=\cos30^\circ$$ $$X=\frac{\sqrt3}{2}$$ Therefore, $$\cos^215^\circ-\sin^215^\circ=\frac{\sqrt3}{2}$$
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