sinA/(sinB+sinC)+sinB/(sinC+sinA) + sinC/(sinA+sinB)=1/(sinB/sinA)+(sinC/sinA)+1/(sinC/sinB)+(sinA/sinB) + 1/(sinA/sinC)+(sinB/sinC)=c/(a+b)+a/(b+c)+b/(a+c)因此只要证明：c/(a+b)+a/(b+c)+b/(a+c)＜2即可...