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: 33



Work Step by Step

$$X=\cos(30^\circ+\theta)$$ We apply the cosine sum identity, which states $$\cos(A+B)=\cos A\cos B-\sin A\sin B$$ $$X=\cos30^\circ\cos\theta-\sin30^\circ\sin\theta$$ $$X=\frac{\sqrt3}{2}\cos\theta-\frac{1}{2}\sin\theta$$ $$X=\frac{\sqrt3\cos\theta-\sin\theta}{2}$$ Therefore, $$\cos(30^\circ+\theta)=\frac{\sqrt3\cos\theta-\sin\theta}{2}$$
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