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: 66


$2\cos^2 \frac{x}{2}\tan x=\tan x+\sin x$

Work Step by Step

Start with the left side: $2\cos^2 \frac{x}{2}\tan x$ Use the half-angle identity for cosine: $=2\left(\pm\sqrt{\frac{1+\cos x}{2}}\right)^2\tan x$ Simplify: $=2*\frac{1+\cos x}{2}*\tan x$ $=(1+\cos x)\tan x$ $=\tan x+\cos x\tan x$ $=\tan x+\cos x*\frac{\sin x}{\cos x}$ $=\tan x+\sin x$ Since this equals the right side, the identity has been proven.
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