Question

if A+C=B then Tan A.tan B.tan C​

Answer 1

Answer:

Step-by-step explanation:

I want to prove

tanA+tanB+tanC=tanAtanBtanCwhen A+B+C=180∘

We know that

tan(A+B)=tanA+tanB1−tanAtanB and that A+B=180∘−C.

Therefore tan(A+B)=−tanC. From here, I get stuck. Please help.

31

Note that

Im(eiπ)=0(1)

Thus, if a+b+c=π,

0=Im(eiaeibeic)=Im((cos(a)+isin(a))(cos(b)+isin(b))(cos(c)+isin(c)))=sin(a)cos(b)cos(c)+cos(a)sin(b)cos(c)+cos(a)cos(b)sin(c)−sin(a)sin(b)sin(c)(2)

Dividing (2) by cos(a)cos(b)cos(c) yields

tan(a)+tan(b)+tan(c)=tan(a)tan(b)tan(c)(3)

Answer 2

Hope that it'll help you