How do I simplify sin((tan^(-1))x)?

1 Answer
Harish Chandra Rajpoot
Jul 25, 2018

#\frac{x}{\sqrt{1+x^2}}#

Explanation:

Let

#\tan^{-1}x=\theta\quad (\forall \ \ -\pi/2\le \theta \le \pi/2)#

#\tan\theta=x#

#\therefore \sin\theta=\frac{\tan\theta}{\sec \theta}#

#\sin\theta=\frac{\tan\theta}{\sqrt{1+\tan^2 \theta}}#

#\sin(\tan^{-1}x)=\frac{x}{\sqrt{1+x^2}}#

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