若f(x)=cos2x-cos(2x+2π/3)-2sin²(x+π/6)+1,则f(x)的最大值是

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若f(x)=cos2x-cos(2x+2π/3)-2sin²(x+π/6)+1,则f(x)的最大值是

若f(x)=cos2x-cos(2x+2π/3)-2sin²(x+π/6)+1,则f(x)的最大值是
若f(x)=cos2x-cos(2x+2π/3)-2sin²(x+π/6)+1,则f(x)的最大值是

若f(x)=cos2x-cos(2x+2π/3)-2sin²(x+π/6)+1,则f(x)的最大值是
因为f(x)=cos2x-cos(2x+2π/3)-2sin²(x+π/6)+1
=cos2x-cos2xcos2π/3+sin2xsin2π/3+cos(2x+π/3)
=cos2x+1/2cos2x+根号3/2sin2x+1/2cos2x-根号3/2sin2x
=2cos2x
所以f(x)的最大值是2,此时cos2x=1.