[" 97."tan^(-1)(1)/(sqrt(x^(2)-1))=],[" (a) "(pi)/(2)+cosec^(-1)x]

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

"tan"^(-1)1/(sqrt(x^(2)-1))|x|gt1

tan^(-1)(x+sqrt(1+x^(2)))=

tan^(- 1)(1/(sqrt(x^2-1))),|x|gt1

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

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

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

Prove that tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2) .

Prove that : tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2)