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 5.6 Half-Angle Identities - 5.6 Exercises - Page 243: 43



Work Step by Step

$$\pm\sqrt{\frac{1+\cos\frac{x}{4}}{2}}$$ From the half-angle identity for cosine: $$\pm\sqrt{\frac{1+\cos\theta}{2}}=\cos\frac{\theta}{2}$$ We can apply the identity to the given expression with $\theta=\frac{x}{4}$. $$\pm\sqrt{\frac{1+\cos\frac{x}{4}}{2}}=\cos\frac{\frac{x}{4}}{2}$$ $$\pm\sqrt{\frac{1+\cos\frac{x}{4}}{2}}=\cos\frac{x}{8}$$
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