A function is said to even if it returns the same output when given two opposite inputs:
[tex] f(x) = f(-x) [/tex]
In your case, you have
[tex] f(x) = 1-\cos(x), \quad f(-x) = 1-\cos(-x) [/tex]
And since [tex] \cos(x) = \cos(-x) [/tex], the proof is concluded.
