If `3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)((2x)/(1-x^2))=pi/3` , then `x` is equal to `1/(sqrt(3))` (b) `-1/(sqrt(3))` (c) `sqrt(3)` (d) `-(sqrt(3))/4`

Explanation

We have given

`3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)((2x)/(1-x^2))=pi/3`

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

Then

`3(2tan^(-1)x)-4(2tan^(-1)x)+2(2tan^(-1)x)=(pi)/3`

`6tan^(−1)x−8tan^(−1)x+4tan^(−1)x=(pi)/3`

`2tan^(-1)x=(pi)/3`

`tan^(-1)x=(pi)/6`

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