If A, B, C are the angles of a triangle such that angle A is obtuse then

A>π/2 B+C<π/2⇒tan⁡(B+C)>0⇒ tan⁡B+tan⁡C1−tan⁡Btan⁡C>0⇒ tan⁡Btan⁡C<1( as tan⁡B,tan⁡C>0)