Prove that `tan^(-1)((3a^2x-x^3)/(a^3-3ax^2))=3tan^(-1)""(x)/a, agt 0 ,(-a)/sqrt3lexlea/sqrt3`

Write the following functions in the simplest form : tan^(-1)((3a^2x - x^3)/(a^3- 3ax^2)), a gt 0, -a/sqrt3 le x le a/sqrt3

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

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

Prove that tan (13pi)/12=2-sqrt3

Prove that sin[2tan^(-1){sqrt((1-x)/(1+x))}]=sqrt(1-x^2)

Prove that tan ^(-1) x+tan ^(-1) ((2 x)/(1-x^2))=tan ^(-1)((3 x-x^3)/(1-3 x^2)),|x|lt1/sqrt3

If tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x , then x =

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