Prove the following: `tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2))`

tan^(-1)x+tan^(-1)(2x)/(1-x^(2))=pi+tan^(-1)(3x-x^(3))/(1-3x^(2)),(x>0)

Prove that : tan^(-1)x +tan^(-1). (2x)/(1-x^(2)) = tan^(-1) . (3x-x^(3))/(1-3x^(2)) , |x| lt 1/(sqrt(3))

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

Prove that: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))

Prove that 3tan^(-1)x=tan^(-1)((3x-x^3)/(1-3x^2))

Solve : tan^(-1) x + tan^(-1)( (2x)/(1-x^2)) = pi/3

tan^(-1)x+(tan^(-1)(2x))/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|<(1)/(sqrt(3))

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

[ If xgt0 then which of the following is true 1) tan^(-1)xgt(x)/(1+x^(2)), 2) tan^(-1)x=(x)/(1+x^(2)) 3) tan^(-1)xlt(x)/(1+x^(2)), 4) tan^(-1)x!=(x)/(1+x^(2))]