Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.4 Double-Angle and Half-Angle Identities - 7.4 Exercises - Page 694: 88


$\frac{1+\cos 2x}{\sin 2x}=\cot x$

Work Step by Step

Start with the left side: $\frac{1+\cos 2x}{\sin 2x}$ Use the double-angle identities $\cos 2x=2\cos^2 x-1$ and $\sin 2x=2\sin x\cos x$: $=\frac{1+2\cos^2 x-1}{2\sin x\cos x}$ Simplify: $=\frac{2\cos^2 x}{2\sin x\cos x}$ $=\frac{\cos x}{\sin x}$ $=\cot x$ Since this equals the right side, the identity has been proven.
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