you forgot to tell us whether or not f(x) is an even function. I assume it isHow does one show that f(x)sin(x) is an even function?odd:

f(-x)sin(-x) =-1*f(x)*-1*sin(x) = f(x)sin(x)

agree.For the odd function g(x)cos(x) I calculate by replacing x by -x ie

g(-x)cos(-x) but cos(-x) = cos (x) therefore

g(-x)cos(x)=-g(x)cos(x) hence odd because g(-x)=-g(x)