已知
（1）求函数f（x）的最小正周期； （2）当x∈[0，
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（1）函数 f(x)=
•a
=2sinxcosx+（cosx+sinx）（cosx-sinx）=2sinxcosx+cos2x-sin2x b
=sin2x=cos2x=
sin（2x+2
），π 4
故函数f（x）的最小正周期等于
=π．2π 2
（2）当x∈[0，
]时，π 2
≤2x+π 4
≤π 4
，故当2x+5π 4
=π 4
时，函数取得最大值为 π 2
，当 2x+2
=π 4
时，函数取得最小值为-1．5π 4
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