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: 42



Work Step by Step

$$\pm\sqrt{\frac{1-\cos 5A}{1+\cos 5A}}$$ Here we notice at the start of the expression, there is the sign $\pm$, which means we do not have to decide whether to take positive or negative square root. From the half-angle identity for tangents: $$\pm\sqrt{\frac{1-\cos\theta}{1+\cos\theta}}=\tan\frac{\theta}{2}$$ We can apply the identity to the given expression with $\theta=5A$. $$\pm\sqrt{\frac{1-\cos5A}{1+\cos5A}}=\tan\frac{5A}{2}$$
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