[" रूप में लिखिए: "],[qquad " 6."tan^(-1)(1)/(sqrt(x^(2)-1)),|x|>1]

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

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

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

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

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

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

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

tan^(-1)((sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)-sqrt(1-x)))

Number of values of x satisfying simultaneously sin^(-1) x = 2 tan^(-1) x " and " tan^(-1) sqrt(x(x-1)) + cosec^(-1) sqrt(1 + x - x^(2)) = pi/2 , is