sinA+sinB =sinA+sin(120°-A) =sinA+sin120°cosA-cos120°sinA =sinA+√3/2 cosA+1/2 sinA =3/2 sinA +√3/2 cosA =√3(√3/2 sinA +1/2 cosA) =√3sin(A+30°) 当A=60°时,sin(A+30°）取最大值1 即sinA+sinB取最大值√3
