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

Solve tan^(-1)x +"tan"^(-1) (2x)/(1-x^(2))=(pi)/(2) .

Prove that "tan"^(-1)(1)/(4) +"tan"^(-1)(2)/(9) =(1)/(2)"tan"^(-1)(4)/(3) .

Solve tan^(-1)x -"tan"^(-1)(1)/(4)=(pi)/(4) .

Solve tan^(-1)(x-1) +tan^(-1) x +tan^(-1)(x+1)= tan^(-1)(3x) .

Solve for x, tan^(-1)((2x)/(1-x^(2)))+cot^(-1)((1-x^(2))/(2x))=(pi)/(3), -1 lt x lt 1 .

Solve "tan"^(-1)(1-x)/(1+x) =(1)/(2) "tan"^(-1)x, x gt 0 .

Express tan^(-1) ((3a^(2)x -x^(3))/( a^(3) -3ax^(2))) , where a gt 0, (-a)/(sqrt(3)) le x le (a)/(sqrt(3)) in the simplest form.

Prove that. tan^(-1)((1)/(4)) +tan^(-1)((2)/(9)) =(1)/(2) cos^(-1) ((3)/(5)) .