设A+B=1,有:M是sinA+sinB的最大值,m是sinA*sinB的最大值,求M^2/m.

sinA+sinB=2sin((A+B)/2)*cos((A-B)/2)=2sin(1/2)*cos((A-B)/2)
当A=B时取得最大值 M=2sin(1/2)
sinA*sinB
=1/2*(cos(A-B)-cos(A+B))
=1/2*(cos(A-B)-cos1)
当A=B时,取得最大值 m=(1-cos1)/2
所以 M^2/m
=(2sin(1/2))^2/((1-cos1)/2)
=4(sin(1/2))^2/(sin(1/2))^2
=4