Definitions

Recall that a function is even if f(-x)=f(x) for all x and a function is odd if f(-x)=-f(x).

You can test if a function is even by checking if f(x)-f(-x)=0.
You can test if a function is odd by checking if f(x)+f(-x)=0

Most people know that cos(x) and sin(x) are the prototypical even and odd functions.


  Simplify[Cos[x]-Cos[-x]]
  Simplify[Sin[x]+Sin[-x]]

Up to Even and Odd Functions