I am asked the following question
For what values of $k$ is $f(x)=\cos(x-k)$
a) even
b) odd
c) neither
I am not quite sure how to tackle this problem, I only got so far as to say, for example in letter a,
$$f(-x) = f(x)$$
$$\cos(-x-k) = \cos(x-k)$$
I'm not sure how to continue from here.
Best Answer
Hint:
Use Prosthaphaeresis Formulas
For the even case,
$$\cos(-x-k)=\cos(x-k)\iff2\sin x\sin k=0$$
As $x$ is arbitrary, $\cos x\ne0\implies\sin k=0$
Similarly for the odd case