Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX D - Trigonometry - D Exercises: 51

Answer

$tan2\theta=\frac{2tan\theta}{1-tan^{2}\theta}$

Work Step by Step

We need to prove the identity $tan2\theta=\frac{2tan\theta}{1-tan^{2}\theta}$ $tan2\theta =tan(\theta+\theta)$ $tan(\theta+\theta)=\frac{tan\theta+tan\theta}{1-tan\theta\times tan\theta}$ [sum identity for tangent] Thus, $tan(\theta+\theta)=\frac{2tan\theta}{1-tan^{2}\theta}$ Hence, $tan2\theta=\frac{2tan\theta}{1-tan^{2}\theta}$
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