Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises: 51

Answer

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

Work Step by Step

Need to prove the identity $tan2\theta=\frac{2tan\theta}{1-tan^{2}\theta}$ Let us take left side solve first. Since , $tan2\theta =tan(\theta+\theta)$ $tan(\theta+\theta)=\frac{tan\theta+tan\theta}{1-tan\theta\times tan\theta}$ [ 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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