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

show that tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2)),|x|<1/sqrt3

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

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

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

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

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

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

Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

Solve: tan^(-1)((x-1)/(x+1))+tan^(-1)((2x-1)/(2x+1))=tan^(-1)((23)/(36))