The correct option is B
4
Here, if we assume tanB=x, then
tanA=2x and tanC=18x.
We know the conditional identity for a triangle ABC.
tanA.tanB.tanC =tanA+tanB+tanC.
Now, substituting the values of 2x+x+18x=2x.x.18x⇒x+20x=36x⇒x=36x−20x⇒x=16x⇒x=4=tanB (∵cotA.cotB=1/2, so tanB>0)
Thus, Option b. is correct.