已知函数f(x)=sin^2x+2倍根号下3sinxcosx+3cos^2x.求函数的单调递增区间

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已知函数f(x)=sin^2x+2倍根号下3sinxcosx+3cos^2x.求函数的单调递增区间

已知函数f(x)=sin^2x+2倍根号下3sinxcosx+3cos^2x.求函数的单调递增区间
已知函数f(x)=sin^2x+2倍根号下3sinxcosx+3cos^2x.求函数的单调递增区间

已知函数f(x)=sin^2x+2倍根号下3sinxcosx+3cos^2x.求函数的单调递增区间
f(x)=sin^2x+2√3sinxcosx+3cos^2x
=(sinx+√3cosx)^2
=[sin(π/6+x)]^2
2kπ

f(x)=sin^2x+2√3sinxcosx+3cos^2x
=(sinx+√3cosx)^2
=[sin(π/6+x)]^2
2kπ<π/6+x<2kπ+π/2 ,2kπ+π<π/6+x<2kπ+3π/2
2kπ-π/6

2倍根号下即是外面用两个根号?