已知函数f(x)=sin(2x-π/6)+cos2x求f(x)的最小周期,求f(X)的单调递减区间

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已知函数f(x)=sin(2x-π/6)+cos2x求f(x)的最小周期,求f(X)的单调递减区间

已知函数f(x)=sin(2x-π/6)+cos2x求f(x)的最小周期,求f(X)的单调递减区间
已知函数f(x)=sin(2x-π/6)+cos2x求f(x)的最小周期,求f(X)的单调递减区间

已知函数f(x)=sin(2x-π/6)+cos2x求f(x)的最小周期,求f(X)的单调递减区间
f(x)=sin(2x-π/6)+cos2x
=sin2xcos(π/6)-cos2xsin(π/6)+2cos2xsin(π/6)
=sin2xcos(π/6)+cos2xsin(π/6)
=sin(2x+π/6)
所以f(x)的最小正周期T=2π/2=π
且当2kπ+π/2≤2x+π/6≤2kπ+3π/2即kπ+π/6≤x≤kπ+2π/3 (k∈Z)时,函数f(x)是减函数
即f(X)的单调递减区间为每一个区间[ kπ+π/6 , kπ+2π/3 ](k∈Z)