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If sin^(-1)((4x)/(x^2+4))+2tan^(-1)(-x/2...

If `sin^(-1)((4x)/(x^2+4))+2tan^(-1)(-x/2)` is independent of `x ,` find the values of x

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`E = sin^(-1) ((4x)/(x^(2) + 4)) + 2 tan^(-1) (-(x)/(2))`
`= sin^(-1) ((2 xx (x)/(2))/(((x)/(2))^(2) + 1)) -2 tan^(-1). (x)/(2)`
`= 0` (For E to be independent of x)
`rArr |(x)/(2)| le 1`
or `|x| le 2 " or " -2 le x le 2`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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  2. Prove that sin^(-1)((2x)/(1+x^2))=tan^(-1)((2x)/(1-x^2))

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