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: 34



Work Step by Step

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