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If f(x)=tan^(-1)x,g(x)=tan^(-1)((1+x)/(1...

If `f(x)=tan^(-1)x,g(x)=tan^(-1)((1+x)/(1-x))" for "|x|lt1`, show that `f'(x)=g'(x)andg(x)-f(x)=pi/4`.

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tan^(-1)((1+x)/(1-x))=(pi)/(4)+tan^(-1)x,x<1