【高中数学题】【在线等】【必采纳】已知函数f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4)

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【高中数学题】【在线等】【必采纳】已知函数f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4)
（1）求函数的最小正周期和对称轴方程
（2）求函数f（x）在区间[-π/12,π/2]值域

f(x)=cos(2x-5π/3)+2sin(x-π/4)sin(x+π/4)
=cos(2x-2π/3-π)+cosπ/2-cos2x 积化和差公式：sinαsinβ=[-cos(α+β)+cos(α-β)]/2
=-cos(2x-2π/3)-cos2x
=sin2xsin2π/3-cos2xcos2π/3-cos2x
=(√3/2)sin2x-(-1/2)cos2x-cos2x
=(√3/2)sin2x-(1/2)cos2x
=sin(2x-π/6)
最小正周期 T=2π/2=π
对称轴为 2x-π/6=2kπ
x=π/12+kπ k=0,1,2.
(2)自己画图即可看出
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