作业帮已知函数f(x)=2cos(x+三分之派）【sin（x+三分之派）-根号3cos（x+三分之派）】,求函数的最小正周期和单调递减区间
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已知函数f(x)=2cos(x+三分之派）【sin（x+三分之派）-根号3cos（x+三分之派）】,求函数的最小正周期和单调递减区间
已知函数f(x)=2cos(x+三分之派）【sin（x+三分之派）-根号3cos（x+三分之派）】,求函数的最小正周期和单调递减区间
已知函数f(x)=2cos(x+三分之派）【sin（x+三分之派）-根号3cos（x+三分之派）】,求函数的最小正周期和单调递减区间
f(x)=2cos(x+π/3)[sin(x+π/3)-√3cos(x+π/3)]
=2cos(x+π/3)sin(x+π/3)-2√3cos²(x+π/3)
=sin(2x+2π/3)-√3[1+cos(2x+2π/3)]
=sin(2x+2π/3)-√3cos(2x+2π/3)-√3
=2[(1/2)sin(2x+2π/3)-(√3/2)cos(2x+2π/3)]-√3
=2sin(2x+2π/3-π/3)-√3
=2sin(2x+ π/3)-√3
最小正周期Tmin=2π/2=π
当2kπ+π/2≤2x+π/3≤2kπ+3π/2 (k∈Z)时,函数单调递减,此时
kπ+π/12≤x≤kπ+7π/12 (k∈Z)
函数的单调递减区间为[kπ+π/12,kπ+7π/12] (k∈Z)
f(x)=2cos(x+π/3)[sin(x+π/3)-√3cos(x+π/3)]，
=2cos(x+π/3)sin(x+π/3)-2√3cos^2(x+π/3)
=sin(2x+2π/3)-√3[2√3cos^2(x+π/3)-1]-√3
=sin(2x+2π/3)-√3cos(2x+2π/3)-√3
=2sin[(2x+2π/3)-π/3]-√3
=2s...
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f(x)=2cos(x+π/3)[sin(x+π/3)-√3cos(x+π/3)]，
=2cos(x+π/3)sin(x+π/3)-2√3cos^2(x+π/3)
=sin(2x+2π/3)-√3[2√3cos^2(x+π/3)-1]-√3
=sin(2x+2π/3)-√3cos(2x+2π/3)-√3
=2sin[(2x+2π/3)-π/3]-√3
=2sin(2x+π/3)-√3
最小正周期=2π/2=π
2x+π/3∈ [2Kπ+π/2,2Kπ+3π/2]单调递减区间
x∈ [Kπ+π/12,2Kπ+7π/12]单调递减区间
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F（X）=平方根3cos ^ x +根，sinxcosx 3/2
=根号3 *（1 + cos2x）/ 2 + 3/2
所以sin2x/2-根F（发送/ 8）
=根号3 *（1 + COS派/ 4）/ 2 +的罪（派/ 4）/ 2 - 3/2的平方根
=平方根3 *（1/2 +的平方根的2/4）+ 2/4-平方根的2分之3的根
=（平方根6 + 2的平方根）/ 4