函数f(x)=sinx(sinx-cosx)的单调递减区间?A[2kπ+π/8,2kπ+5/8π] B[kπ+π/8,kπ+5/8π] C[2kπ-3/8π,2kπ+π/8] D[kπ-3/8π,kπ+π/8] (全部k属于Z)

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函数f(x)=sinx(sinx-cosx)的单调递减区间?A[2kπ+π/8,2kπ+5/8π] B[kπ+π/8,kπ+5/8π] C[2kπ-3/8π,2kπ+π/8] D[kπ-3/8π,kπ+π/8] (全部k属于Z)

函数f(x)=sinx(sinx-cosx)的单调递减区间?A[2kπ+π/8,2kπ+5/8π] B[kπ+π/8,kπ+5/8π] C[2kπ-3/8π,2kπ+π/8] D[kπ-3/8π,kπ+π/8] (全部k属于Z)
函数f(x)=sinx(sinx-cosx)的单调递减区间?
A[2kπ+π/8,2kπ+5/8π] B[kπ+π/8,kπ+5/8π] C[2kπ-3/8π,2kπ+π/8] D[kπ-3/8π,kπ+π/8] (全部k属于Z)

函数f(x)=sinx(sinx-cosx)的单调递减区间?A[2kπ+π/8,2kπ+5/8π] B[kπ+π/8,kπ+5/8π] C[2kπ-3/8π,2kπ+π/8] D[kπ-3/8π,kπ+π/8] (全部k属于Z)
f(x)=(sinx)^2-sinxcosx=(1-cos2x)/2-(sin2x)/2=-(sin2x+cos2x)/2+1/2=-(根号2)sin(2x+π/4)/2+1/2
2x+π/4在[-π/2+2kπ,π/2+2kπ]递减(注意,上一行的前面有个负号)
所以递减区间为[-3π/8+kπ,π/8+2kπ]