Prove that `tan^(- 1)((6x-8x^3)/(1-12 x^2))-tan^(- 1)((4x)/(1-4x^2))=tan^(- 1)2x ;|2x|<1/(sqrt(3))`

Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))=tan^(-1)2x;|2x|<(1)/(sqrt(3))

Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))= tan^(-1)2x,|2x| lt (1)/(sqrt(3)) .

Prove that : tan^-1((6x-8x^3)/(1-12x^2))- tan^-1(4x/(1-4x^2)) = tan^-1 2x,|2x| < 1/sqrt3

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

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

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

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

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

Prove that tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1

Prove that : 1/6tan^(-1)""(2x)/(1-x^2)+1/9tan^(-1)""(3x-x^2)/(1-3x^2)+1/12 tan^(-1)""(4x-4x^3)/((1-6x^2+x^4))= tan^(-1)x