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: 39



Work Step by Step

$$\pm\sqrt{\frac{1+\cos18x}{2}}$$ 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 cosines: $$\pm\sqrt{\frac{1+\cos A}{2}}=\cos\frac{A}{2}$$ We can apply the identity to the given expression with $A=18x$. $$\pm\sqrt{\frac{1+\cos18x}{2}}=\cos\frac{18x}{2}$$ $$\pm\sqrt{\frac{1+\cos18x}{2}}=\cos9x$$
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