已知函数f(x)=(1+cos2x)sin平方x,x属于R,则f(x)的周期?奇偶?

f(x)=(1+cos2x)(sinx)^2
=2(cosx)^2(sinx)^2
=(1/2)[sin(2x)]^2
=(1/2)[1-cos(4x)]/2
=(1/4)[1-cos(4x)]
=1/4-cos(4x)/4
最小正周期为π/2 ,周期为kπ/2.
f(-x)=1/4-cos(-4x)/4=1/4-cos(4x)/4=f(x)
函数是偶函数.