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  4. Find the value of sin (2 tan -1x), |x| le 1

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Q. Find the value of $ \sin \,(2\,{{\tan }^{-1}}x),\,|x|\le 1 $

J & K CETJ & K CET 2014Inverse Trigonometric Functions

Solution:

$ \sin (2{{\tan }^{-1}}x)=\sin \left( {{\sin }^{-1}}\frac{2x}{1+{{x}^{2}}} \right) $
$ =\frac{2x}{1+{{x}^{2}}},-1\le x\le 1 $