已知函数f(x)=cos^4x+2√3sinxcosx-sin^4x
问题描述:
已知函数f(x)=cos^4x+2√3sinxcosx-sin^4x
求f(x的最小正周期!
答
f(x) = (cosx)^4-(sinX)^4+2√3sinxcosx
= [(cosx)^2+(sinx)^2] [(cosx)^2-(sinx)^2]+√3sin2x
= (cosx)^2-(sinx)^2+√3sin2x
= cos2x+√3sin2x = 2sin(2x+π/6)
最小正周期是π