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______.

f(x)=cosx(sinx+cosx)
=cosxsinx+cos2x
=

1
2
sin2x+
1
2
(cos2x+1)
=
2
2
sin(2x+
π
4
)+
1
2

∵ω=2,∴T=
2
=π.
故答案为:π