1991 AHSME Problems/Problem 21

For all real numbers $x$ except $x=0$ and $x=1$ the function $f(x)$ is defined by $f(x/(1-x))=1/x$ . Suppose $0\leq t\leq \pi/2$ . What is the value of $f(\sec^2t)$ ? These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.