函数f(x)=sin(2x+π6)cos(2x-π3)的最小正周期为π2π2.-数学

题目简介

函数f(x)=sin(2x+π6)cos(2x-π3)的最小正周期为π2π2.-数学

题目详情

函数f(x)=sin(2x+
π
6
)cos(2x-
π
3
)的最小正周期为
π
2
π
2
题型:填空题难度:中档来源:不详

答案

函数f(x)=sin(2x+class="stub"π
6
)cos(2x-class="stub"π
3

=sin[class="stub"π
2
+(2x-class="stub"π
3
)]cos(2x-class="stub"π
3

=-cos2(2x-class="stub"π
3

=-
1+cos(4x-class="stub"2
3
π)
2

=-class="stub"1
2
-class="stub"1
2
cos(4x-class="stub"2
3
π
),
∵ω=4,
∴T=class="stub"2π
4
=class="stub"π
2
,即函数的最小正周期为class="stub"π
2

故答案为:class="stub"π
2

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