已知函数F(X)=2sin²(π/4+X)-√3cos2x-1,x∈R,求f(X)的最小正周期

问题描述:

已知函数F(X)=2sin²(π/4+X)-√3cos2x-1,x∈R,求f(X)的最小正周期

f(x)=2sin^2 (x+π/4)-√3cos2x-1
=-cos(2x+π/2)-√3cos2x
=sin2x-√3cos2x
=2sin(2x-π/3)
当x属于R时,函数f(x)的最小正周期T=2π/2=π