[" 20.(i) "tan^(-1)(sqrt(1+a^(2)x^(2))-1)/(ax)],[" (ii) "tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))]

If tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))=k tan^(-1)(x/a) then k=

If y = Tan^(-1)((3a^2x-x^3)/(a^3-3ax^2)) then (dy)/(dx)=

int(1+tan^(2)x)/(sqrt(tan^(2)x+3))

Prove that tan^(-1)""(3a^(2)x-x^(3))/(a^(3)-3ax^(2))=3tan^(-1)""x/a .

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

Prove that: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))

Write the following in the simplest form: tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))

If x lt -(1)/sqrt(3) , then tan^(-1)(3x-x^(3))/(1-3x^(2)) equals

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

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