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1991 AMC 12 Question 21

AMC12 · 1991 AMC 12

Question 21

If $$
f\left(\frac{x}{x-1}\right)=\frac1x
$$ for all $x\notin\{0,1\},$ and $0\lt\theta\lt\frac{\pi}{2},$ then $f(\sec^2\theta)=$
  1. $\sin^2\theta$
  2. $\cos^2\theta$
  3. $\tan^2\theta$
  4. $\cot^2\theta$
  5. $\csc^2\theta$