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 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 218: 10


$$\cos(-15^\circ)=\frac{\sqrt 6+\sqrt 2}{4}$$

Work Step by Step

$$A=\cos(-15^\circ)$$ We can rewrite $-15^\circ$ into the difference of $30^\circ$ and $45^\circ$, which means $$A=\cos(30^\circ-45^\circ)$$ Now we apply the identity for cosine of a difference: $$A=\cos30^\circ\cos45^\circ+\sin30^\circ\sin45^\circ$$ $$A=\frac{\sqrt 3}{2}\frac{\sqrt 2}{2}+\frac{1}{2}\frac{\sqrt 2}{2}$$ $$A=\frac{\sqrt 6}{4}+\frac{\sqrt 2}{4}$$ $$A=\frac{\sqrt 6+\sqrt 2}{4}$$
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