f(x)=sinx(sinx-cosx)的单调区间

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f(x)=sinx(sinx-cosx)的单调区间

f(x)=sinx(sinx-cosx)的单调区间
f(x)=sinx(sinx-cosx)的单调区间

f(x)=sinx(sinx-cosx)的单调区间
f(x)=sin^2x-sinxcosx
=(1-cos2x)/2-(sin2x)/2
=1/2-(1/2)(sin2x+cos2x)
=1/2-√2/2sin(2x+π/4)
1)单调增区间
π/2+2kπ<=2x+π/4<=3π/2+2kπ
π/4+2kπ<=2x<=5π/4+2kπ
π/8+kπ<=x<=5π/8+kπ
2)单调减区间
-π/2+2kπ<=2x+π/4<=π/2+2kπ
-3π/4+2kπ<=2x<=π/4+2kπ
-3π/8+kπ<=x<=π/8+kπ