已知函数f(x)=√3sin^2x+sinxcosx-√3/2(x∈R).(1)若x∈(0,π/2),求f (x)的最大值.

问题描述:

已知函数f(x)=√3sin^2x+sinxcosx-√3/2(x∈R).(1)若x∈(0,π/2),求f (x)的最大值.

f(x)=根号3sin^2x+sinxcosx-根号3/2
=sinxcosx-√3/2*(1-2sin²x)
=(1/2)sin2x-(√3/2)cos2x
=sin(2x)*cos(π/3)-cos(2x)sin(π/3)
=sin(2x-π/3)
如0