∵f（x）=（cos2xcosx+sin2xsinx）sinx=cos2xcosxsinx+sin2xsin²x

=

1

2

sin2xcos2x+

sin2x(1-cos2x)

2

=

sin4x

4

+

sin2x-sin2xcos2x

2

=

1

2

sin2x

由周期公式可得T=π，且f（-x）=

1

2

sin（-2x）=-

1

2

sin2x，即函数f（x）为奇函数

故选A