f(A)＝√3/2-√3sin²A-sinAcosA
=√3/2-√3/2(1-cos2A)-1/2sin2A
=√3/2cos2A-1/2sin2A
=cos(2A+π/6)
A在[π/4,2π/3]
2A+π/6在[5π/6,3π/2]上最小值=-1,最大值=0
2)f(A)=cos(2A+π/6)=0
2A+π/6=π/2 或2A+π/6=3π/2
A=π/6 或A=2π/3(舍去)
B=π-7π/12-π/6=π/4
b/sinB=a/sinA
b=sinBa/sinA=sinπ/4*√6/sinπ/6 =√2/2*√6/1/2=2√3