AHSME 1991 Problem 21

For all real numbers $x$ except $x=0$ and $x=1$ the function $f(x)$ is defined by $f(x/(x-1))=1/x$. Suppose $0\leq t\leq \pi/2$. What is the value of $f(\sec^2t)$? $\text{(A) } sin^2\theta \text{(B) } cos^2\theta \text{(C) } tan^2\theta \text{(D) } cot^2\theta \text{(E) } csc^2\theta$