MathDB

Consider a pyramid

P-ABCD

whose base

ABCD

is a square and whose vertex

P

is equidistant from

A

B

C

, and

D

. If

AB=1

and

\angle APD=2\theta

then the volume of the pyramid is

\text{(A)} \ \frac{\sin \theta}{6} \qquad \text{(B)} \ \frac{\cot \theta}{6} \qquad \text{(C)} \ \frac1{6\sin \theta} \qquad \text{(D)} \ \frac{1-\sin 2\theta}{6} \qquad \text{(E)} \ \frac{\sqrt{\cos 2\theta}}{6\sin \theta}

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