Evaluate for x 1 tansec1 x tansec1 x1 Solutiontan sec1 x

Evaluate for x > 1: tan(sec^-1 (x)) = tan(sec^-1 (x/1)) = ???

Solution

tan (sec^-1 x) = tan(sec^-1 (x/1))

sec^2x = 1+tan^2 x

tan x = sqrt[sec^2 x – 1]

Then tan (sec^-1 x) = sqrt[sec^2 (sec^-1 x) – 1]

= sqrt[(sec (sec^-1 x))^2 - 1] = sqrt(x^2 - 1)