f(x)=( 1+cos2x)sin？ x =( 1+cos2x)( 1-cos2x)/2 = 1/2-cos？ 2x/2

Because? 2x=( 1+cos4x)/2

So f (x) =1/2-1/4-cos4x/4 =1/4-cos4x/4.

T=2π/4=π/2

Cos4x is an even function, so f(x)=f(-x).

F(x) is an even function.