If A,B,C are angles of a triangle such that A is obtuse then
tanAtanB>1
tanBtanC<1
tanCtanA>1
tanAtanBtanC>1
A is obtuse⇒B+C<90° ⇒tanB+C>0 ⇒tanB+tanC1-tanBtanC>0 ⇒1-tanBtanC>0 ⇒tanBtanC<1