Question

in a triangle tan A +tan B+ tan C = 6 and tanA×tan B =2 then find value of tan A ,tan B , tan C​

Answer 1

Answer:

A+B+C=180

A+B=180−C

tan(A+B)=−tanC

(1−tanAtanB)

(tanA+tanB)

=−tanC

tanA+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.

Therefore, it is acute angled triangle.