f(x)=(sinx-cosx)sin2x/sinx.求最小正周期和f(x)的单调增区间

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f(x)=(sinx-cosx)sin2x/sinx.求最小正周期和f(x)的单调增区间

f(x)=(sinx-cosx)sin2x/sinx.求最小正周期和f(x)的单调增区间
f(x)=(sinx-cosx)sin2x/sinx.求最小正周期和f(x)的单调增区间

f(x)=(sinx-cosx)sin2x/sinx.求最小正周期和f(x)的单调增区间
f(x)=(sinx-cosx)sin2x/sinx.=
=2cosx(sinx-cosx)
=sin2x-2cos²x
=sin2x-(1+cos2x)
=sin2x-cos2x-1
=√2(√2/2sin2x -√2/2cos2x)-1
=√2sin(2x-π/4)-1
最小正周期T=2π/2=π
由-π/2+2kπ≤2x-π/4≤π/2+2kπ
-π/8+kπ≤x≤3π/8+kπ
所以原函数的单调增区间为:
【-π/8+kπ,3π/8+kπ】

得f(x)=sin2x-cos2x-1=根号2*sin(2x-pi/4)-1;在求的T=pi;