I need help with this question

Question

If 0≤u<pi/2 and x=secu, then √x^2−1=f(u), where
f(u)=

Answer 1

Below I have inserted grouping symbols (brackets) in order to make the problem meaningful and correct:

 

If 0≤u<pi/2 and x=secu, then √[x^2−1]=f(u)

Therefore f(u) = square root of [sec²u - 1]  = square root of [(1-cos²u)/cos²u] =

square root of [sin²u / cos²u] = 

tan u.