In a ΔleABC,tanA2,TanB2TanC2 are in H.P. then the value of cot (A2).cot(C2)=
3
tanA2,TanB2,TanC2inHP⇒2TanB2=1TanA2+1TanC2⇒2TanA2TanC2=TanB2TanC2+TanB2tanA2
[InΔABC,tanA2TanB2+tanB2tanC2+tanC2tanA2=1]
=2TanA2tanC2=1−tanA2tanC2=3TanA2tanC2=1=tanA2tanC2=13⇒cotA2cotC2=3.