Let \( p \) be the product of the sines of the angles of a triangle...

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Let \( p \) be the product of the sines of the angles of a triangle \( A B C \) and \( q \) is the product of the cosines of the angles.
\( \mathrm{P} \) \( \tan A \tan B+\tan B \tan C+\tan C \tan A \) is equal to

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(A) \( 1+q \)
(B) \( \frac{1+q}{q} \)
(C) \( 1+p \)
(D) \( \frac{1+p}{p} \)
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