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prove that, 2 tan^(-1) 2x = sin^(-1).(4x...

prove that, `2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))`

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The correct Answer is:
`-(1)/(2) le x le (1)/(2)`
`2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2)) = sin^(-1).(2(2x))/(1 + (2x)^(2))`
`rArr -(pi)/(2) le 2 tan^(-1) 2x le (pi)/(2)`
`rArr -(pi)/(4) le tan^(-1) 2x le (pi)/(4)`
`rArr -1 le 2x le 1`
`rArr -(1)/(2) le x le (1)/(2)`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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  3. prove that, 2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))

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