函数f(x)=sin^4x+2根号3sinxcosx-cos^4x的值域为
问题描述：
函数f(x)=sin^4x+2根号3sinxcosx-cos^4x的值域为
答
y=sin^4(x)+2√3(sinxcosx)-cos^4(x) =sin^4(x)-cos^4(x)+2√3sinxcosx =(sin^2x+cos^2x)(sin^2x-cos^2x)+2√3(sinxcosx) =2√3(sinxcosx)-cos2x =√3sin2x-cos2x =2sin(2x-π/6)∴值域是[-2,2]