函数f(x)=cosx(sinx+cosx)(x∈R)的最小正周期是_.
问题描述:
函数f(x)=cosx(sinx+cosx)(x∈R)的最小正周期是______.
答
f(x)=cosx(sinx+cosx)
=cosxsinx+cos2x
=
sin2x+1 2
(cos2x+1)1 2
=
sin(2x+
2
2
)+π 4
,1 2
∵ω=2,∴T=
=π.2π 2
故答案为:π