Question

If in a triangle ABC, tanA+tanB+tanC=6 and tanAtanB=2 then sinAsinBsinC equals?

Answer 1

Step-by-step explanation:

A+B+C=180A+B=180−Ctan(A+B)=−tanC(1−tanAtanB)(tanA+tanB)=−tanCtanA+tanB+tanC=tanAtanBtanC=6

Now, tanC=3. So, the angle C is acute.

tanA+tanB=3

tanA.tanB=2

∴tanA=2,tanB=1

A and B are also acute.