已知函数f(x)=sin^3xcosx+cos^3xsinx+√3sin^2x求函数的单调减区间求y=(x)(0≤x≤

f(x)=sin³xcosx+cos³xsinx+√3 sin²x
=sinxcosx(sin²x+cos²x)+√3 (1-cos2x)/2
=½ sin2x - √3 /2 cos2x + √3 /2
=sin(2x-π/3) + √3 /2
f(x) 的递减区间是 2x-π/3∈[π/2+kπ,3π/2+kπ] (k∈Z)
即 x∈[5π/12+kπ/2,11π/12+kπ/2] (k∈Z)
在 0≤x≤π 内的单调递减区间是 x∈[5π/12,11π/12]
值域是 [√3 /2 - 1,√3 /2 + 1]

已知函数f(x)=sin³xcosx+cos³xsinx+(√3)sin²x，求函数的单调减区间，求y=f(x)(0≤x≤ π ）的值域
f(x)=sinxcosx(sin²x+cos²x)+(√3/2)(1-cos2x)=(1/2)sin2x-(√3/2)cos2x+(√3)/2
=sin2xcos(π/3)-cos2xsin(π...

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