According to Vieta, tan(A)+tan(B) = p, tan(A)*tan(B) = q and cot(A)+cot(B) = r, cot(A)*cot*B)=s.

Therefore, r*s = (cot(A)+cot(B))*cot(A)*cot(B) = (1/tan(A)+1/(tan(B))/(tan(A)*tan(B))

= p/q^2