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 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 227: 35



Work Step by Step

$$X=\cos(60^\circ+\theta)$$ To expand the formula, cosine sum identity would be used: $$\cos(A+B)=\cos A\cos B-\sin A\sin B$$ That means $$X=\cos60^\circ\cos\theta-\sin60^\circ\sin\theta$$ $$X=\frac{1}{2}\cos\theta-\frac{\sqrt3}{2}\sin\theta$$ $$X=\frac{\cos\theta-\sqrt3\sin\theta}{2}$$ Therefore, $$\cos(60^\circ+\theta)=\frac{\cos\theta-\sqrt3\sin\theta}{2}$$
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