[:'tan^(-1)((3x-x^(3))/(1-3x^(2)))=3tan^(-1)x]

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

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

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

If y = tan ^(-1) ((2x )/( 1 -x ^(2))) + tan ^(-1) ((3x - x ^(3))/( 1 - 3x ^(2)))- tan ^(-1) ((4x - 4x ^(3))/( 1 - 6x + x ^(4))), then show that (dy)/(dx) = (1)/(1 + x ^(2)).

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

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

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

Differentiate tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|<(1)/(sqrt(3)) w.r.t tan ^(-1)((x)/(sqrt(1-x^(2))))