If (sin A) / (sin B) = p and (cos A) / (cos B) = q, find tan A and tan B

The answer:

tan A = sin A) / cos A, but sin A) / (sin B) = p implies sin A = psin B, and

cos A) / (cos B) = q implies cos A = q cos B

so tan A = psin B / q cos B = p/q (tanB), so tanA = p/q tanB or tanB = q/p tanA