(2014•丰台区一模)已知函数f(x)=cos(2x-π3)-2sin2x+1.
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(2014•丰台区一模)已知函数f(x)=cos(2x-
π |
3 |
![(2014•丰台区一模)已知函数f(x)=cos(2x-π3)-2sin2x+1.](/uploads/image/z/18300853-37-3.jpg?t=%EF%BC%882014%E2%80%A2%E4%B8%B0%E5%8F%B0%E5%8C%BA%E4%B8%80%E6%A8%A1%EF%BC%89%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dcos%EF%BC%882x-%CF%803%EF%BC%89-2sin2x%2B1%EF%BC%8E)
(Ⅰ)∵f(x)=cos2xcos
π
3+sin2xsin
π
3+cos2x
=
1
2cos2x+
3
2sin2x+cos2x
=
3
2sin2x+
3
2cos2x
=
3(
1
2sin2x+
3
2cos2x)
=
3sin(2x+
π
3)
∴f(x)的最小正周期为π.
(Ⅱ)由(Ⅰ)知f(x)=
3sin(2x+
π
3),
∴当x∈[0,
π
3+sin2xsin
π
3+cos2x
=
1
2cos2x+
3
2sin2x+cos2x
=
3
2sin2x+
3
2cos2x
=
3(
1
2sin2x+
3
2cos2x)
=
3sin(2x+
π
3)
∴f(x)的最小正周期为π.
(Ⅱ)由(Ⅰ)知f(x)=
3sin(2x+
π
3),
∴当x∈[0,
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