If tan-1x=2tan-1(1-x1+x), then the value of x is ______ - Mathematics

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If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______ 

Options

  • `1/sqrt3`

  • `sqrt3`

  • 1

  • -`sqrt3`

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Solution

If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is `underline(1/sqrt3)`.

Explanation:

`tan^-1x = 2tan^-1((1 - x)/(1 + x))`

⇒ `1/2tan^-1x = tan^-1((1 - x)/(1 + (1)(x)))`

⇒ `1/2tan^-1 = tan^-1(1) - tan^-1x`

⇒ `1/2tan^-1x = pi/4 - tan^-1x`

⇒ `1/2tan^-1x + tan^-1x = pi/4` 

⇒ `tan^-1x = pi/6`

⇒ `x = tan  pi/6 = 1/sqrt3`

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