Question

Explain why the function y=1-cosx is an even function

Answer 1

A function is said to even if it returns the same output when given two opposite inputs:

`f(x) = f(-x)`

In your case, you have

`f(x) = 1-\cos(x), \quad f(-x) = 1-\cos(-x)`

And since
`\cos(x) = \cos(-x)`, the proof is concluded.