Folks,

How does one show that f(x)sin(x) is an even function?

I attempt it be replacing x by -x ie

f(-x)sin(-x) but sin(-x) =-sin(x) therefore

f(-x)(-sin(x))=-f(-x)sin(x)?????

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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)