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1983 AMC 12 Question 20

AMC12 · 1983 AMC 12

Question 20

If $\tan\alpha$ and $\tan\beta$ are the roots of $x^2-px+q=0,$ and $\cot\alpha$ and $\cot\beta$ are the roots of $x^2-rx+s=0,$ then $rs$ is necessarily
  1. $pq$
  2. $\frac1{pq}$
  3. $\frac{p}{q^2}$
  4. $\frac{q}{p^2}$
  5. $\frac pq$