Answer
$\tan 4\theta$
Work Step by Step
Comparing with the Half-Angle Identity
$\displaystyle \tan\frac{A}{2}=\pm\sqrt{\frac{1-\cos A}{1+\cos A}}$,
if we define $ A=8\theta$,
the RHS equals the given expression.
So, the LHS =$ \tan 4\theta$
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
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: 75
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