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: 12



Work Step by Step

$$\cos105^{\circ}$$ As in the hint: $$105^\circ=60^\circ+45^\circ$$ That means $$\cos105^\circ=\cos(60^\circ+45^\circ)$$ Now we apply cosine of a sum: $$\cos105^\circ=\cos60^\circ\cos45^\circ-\sin60^\circ\sin45^\circ$$ $$\cos105^\circ=\frac{1}{2}\frac{\sqrt2}{2}-\frac{\sqrt3}{2}\frac{\sqrt2}{2}$$ $$\cos105^\circ=\frac{\sqrt2}{4}-\frac{\sqrt6}{4}$$ $$\cos105^\circ=\frac{\sqrt2-\sqrt6}{4}$$
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