Prove that $\cos^2t$ is a characteristic function.
I really do not understand how to prove this.
I know that if it is a characteristic function, it must fulfill some properties.
But so far in all the examples we have seen in class, to prove that something is a characteristic function, we have seen that it can be written as a combination of known features.
Now, if I do not have the ability to see that it comes from something known (maybe we have not seen it in class), how can I see it?