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1990 AMC 12 Question 21

AMC12 · 1990 AMC 12

Question 21

Consider a pyramid $P\text{-}ABCD$ whose base $ABCD$ is square and whose vertex $P$ is equidistant from $A,$ $B,$ $C,$ and $D.$ If $AB=1$ and $\angle APB=2\theta,$ then the volume of the pyramid is
  1. $\frac{\sin\theta}{6}$
  2. $\frac{\cot\theta}{6}$
  3. $\frac1{6\sin\theta}$
  4. $\frac{1-\sin2\theta}{6}$
  5. $\frac{\sqrt{\cos2\theta}}{6\sin\theta}$