Answer
$\frac{24}{7}$
Work Step by Step
1. Let $tan^{-1}(\frac{3}{4})=t$, we have $tan(t)=\frac{3}{4}$
2. $tan(2tan^{-1}(\frac{3}{4}))=tan(2t)=\frac{2tan(t)}{1-tan^2(t)}=\frac{2(\frac{3}{4})}{1-(\frac{3}{4})^2}=\frac{24}{7}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.6 Double-angle and Half-angle Formulas - 6.6 Assess Your Understanding - Page 519: 84
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