Question

For all real numbers x, except x = 0 and x=1, the function f is defined by f(x/(x - 1))=1/x. Suppose 0 < theta < pi / 2, What is f((sec(theta))^2)

Answer 1

if x = csc^2θ, then
x/(x-1) = csc^2θ/(csc^2θ-1) = csc^2θ/cot^2θ = sec^2θ
so I guess then that
f(sec^2θ) = csc^2θ