0quad AAquad tan^(-1)(1)/(sqrt(x^(2)-1)),|x|>1

tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=

If tan^(-1)(sqrt(1+x^(2))-1)/x=4^(0) , then

If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then

Differentiate tan^(-1)((sqrt(1+x^(2)-1))/(x)) with respect to tan^(-1)x,x!=0

Differentiate the following functions with respect to x:tan^(-1){sqrt(1+x^(2))-x},x in R (ii) tan^(-1){(sqrt(1+x^(2))-1)/(x)},x!=0

Write each of the following in the simplest form: tan^(-1){sqrt(1+x^(2))-x},x in R (ii) tan^(-1){(sqrt(1+x^(2))-1)/(x)},x!=0

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

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