Precalculus (6th Edition)

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

Chapter 7 - Trigonometric Identities and Equations - Chapter 7 Test Prep - Review Exercises - Page 737: 59


$2\tan x\csc 2x-\tan^2 x=1$

Work Step by Step

Start with the left side: $2\tan x\csc 2x-\tan^2 x$ Simplify: $=2*\frac{\sin x}{\cos x}*\frac{1}{\sin 2x}-\tan^2 x$ $=2*\frac{\sin x}{\cos x}*\frac{1}{2\sin x\cos x}-\tan^2 x$ $=\frac{2\sin x}{2\sin x\cos^2 x}-\tan^2 x$ $=\frac{1}{\cos^2 x}-\tan^2 x$ $=\sec^2 x-\tan^2 x$ $=1$ Since this equals the right side, the identity has been proven.
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