函数f(x)=2sin2x-2sinxcosx-根号3cos2x求最小正周期和最值
问题描述：
函数f(x)=2sin2x-2sinxcosx-根号3cos2x求最小正周期和最值
答
f(x)=2sin2x-2sinxcosx-√3cos2x
=2sin2x-sin2x-√3cos2x
=sin2x-√3cos2x
=2(1/2sin2x-√3/2cos2x)
=2sin(2x+ψ)
T=2π/2=π
f(x)max=2 f(x)min=-2当x=多少时有最大最小=2sin(2x+ψ)=2sin(2x-π/3)2x-π/3=π/2+2kπ2x=5π/6+2kπx=5π/12+kπ k=0,1,2……有最大值2x-π/3=-π/2+2kπ2x=-π/6+2kπx=-π/12+kπk=0,1,……2有最小值.