Question

If A + B + C = 180, then tan (A + B/2) = _____.​

Answer 1

Answer:

According to the question we know that

A+B+C =180

So,

=> A+B=180-C

Let multiply by tan we found that

=> tan(A+B) = tan(180-C)

(tana + tanb)/(1 - tana \: tanb)} = - tanc

=> tanA+tanB = -tanC(1-tanA tanB)

=> tanA+tanB= - tanC+tanA tanB tanC

=> tanA +tanB +tanC = tanA tanB tanC

Hence proved