" mple "13." If "x=(1)/(sqrt(3)-sqrt(2))" ,prove that "x^(3)+(1)/(x^(3))+2(x^(2)+(1)/(x^(2)))-9(x

If y = tan ^ (- 1) ((3x) / (1-2x ^ (2))), - (1) / (sqrt (2))

If x=sqrt(3)-sqrt(2) then (1)/(x^(3))-x^(3)=

If x = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2)) , find the value of x^(2) + (1)/(x^(2)) .

If x=(sqrt(2)+1)^(-1/3) , then prove that (x-x^(-1))^3+3(x-x^(-1))+2=0 .

If y=(x cos^(-1)x)/(sqrt(1-x^(2)))-log sqrt(1-x^(2)), then prove that (dy)/(dx)=(co^(1-x)x)/((1-x^(2))^((3)/(2)))

if x=sqrt(3)+(1)/(sqrt(3)) and y=sqrt(3)-(1)/(sqrt(3)) then x^(2)-y^(2) is

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}

Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " -(1)/(sqrt3) lt x lt (1)/(sqrt3)),(pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x gt (1)/(sqrt3)),(-pi + tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if " x lt - (1)/(sqrt3)):}