Question

if A+B+C=π and sin(A+C/2)=nsinC/2 , then show that tanA/2 tanB/2=n-1/n+1​

Answer 1

Answer:

let consider A=B=C=π/3

SO sin(π/3+π/6)=(2)sin(π/6)

so n=2;

tan(π/6)tan(π/6)=(1/√3)(1/√3)=1/3

as n=2

2-1/2+1=1/3

hence proved