Write the following in the simplest form : tan^-1{2(x)^1/2/(1-x)}

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Solution

Dear Student,

$We are given \tan^{- 1} [\frac{2 \sqrt{x}}{1 - x}] eq (1) Put x = \tan^{2} (y) \Rightarrow \sqrt{x} = \tan (y) \Rightarrow y = \tan^{- 1} (\sqrt{x}) Eq (1) becomes \tan^{- 1} [\frac{2 \tan (y)}{1 - \tan^{2} (y)}] = \tan^{- 1} (\tan (2 y)) = 2 y = 2 \tan^{- 1} (\sqrt{x})$

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