f(x)=sin x (sinx-cosx)的减单调区间?f(x)=sin x (sinx-cosx)的单调区间解如下：f（x）=sin^2 X - sinxcosx=2sinxcosx-sinxcox=sinxcox=1/2sin 2xsinx的单调减区间：π/2+2kπ < x < 3π/2+2kππ/2+2kπ < 2x < 3π/2+2kππ/4+kπ< X < 3π/4

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f(x)=sin x (sinx-cosx)的减单调区间?f(x)=sin x (sinx-cosx)的单调区间解如下：f（x）=sin^2 X - sinxcosx=2sinxcosx-sinxcox=sinxcox=1/2sin 2xsinx的单调减区间：π/2+2kπ < x < 3π/2+2kππ/2+2kπ < 2x < 3π/2+2kππ/4+kπ< X < 3π/4
f(x)=sin x (sinx-cosx)的减单调区间?
f(x)=sin x (sinx-cosx)的单调区间
解如下：
f（x）=sin^2 X - sinxcosx
=2sinxcosx-sinxcox
=sinxcox
=1/2sin 2x
sinx的单调减区间：π/2+2kπ < x < 3π/2+2kπ
π/2+2kπ < 2x < 3π/2+2kπ
π/4+kπ< X < 3π/4+kπ
[ kπ-3/8π ,kπ-π/8 ]
请问我哪里算错了?

f(x)=sin x (sinx-cosx)的减单调区间?f(x)=sin x (sinx-cosx)的单调区间解如下：f（x）=sin^2 X - sinxcosx=2sinxcosx-sinxcox=sinxcox=1/2sin 2xsinx的单调减区间：π/2+2kπ < x < 3π/2+2kππ/2+2kπ < 2x < 3π/2+2kππ/4+kπ< X < 3π/4
f（x）=sin^2 X - sinxcosx
=2sinxcosx-sinxcox错
=(cos2x+1)/2-sinxcox
=1/2cos2x-1/2sin2x+1/2
=√2/2sin(π/4-2x)+1/2
单调减区间：
π/2+2kπ < π/4-2x< 3π/2+2kπ
-5π/8+kπ < x< -π/8+kπ
单调递增区间
-π/2+2kπ < π/4-2x< π/2+2kπ
-π/8+kπ < x < 3π/8+kπ

sin^2 X=2sinxcosx错了
应为(1-COS2X)/2

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