1
f(x)=2sinx(cosxcosπ/3-sinxsinπ/3)
=sinxcosx-√3sin²x
=1/2sin2x-√3/2(1-cos2x)
=1/2sin2x+√3/2cos2x-√3/2
=sin(2x+π/3)-√3/2
f(x)的最小正周期T=2π/2=π
2
∵a,b,c成等比数列
∴b²=ac
根据余弦定理:
cosB=(a²+c²-b²)/(2ac)
=(a²+c²-ac)/(2ac)
∵a²+c²≥2ac
∴(a²+c²-ac)/(2ac)≥(2ac-ac)/(2ac)=1/2
即cosB≥1/2
∴0