A＋B＝120度,那么sinA＋sinB的最大值是多少?

A+B=120°,
sinA+sinB
=sinA+sin(120°-A)
= sinA+sin120°cos A -cos120°sin A
= sinA+√3/2 cos A+1/2 sin A
=3/2 sin A+√3/2 cos A
=√3(√3/2 sin A+1/2 cos A)
=√3sin(A+30°)
因为0°