How to show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$ I am trying to solve the following exercise:


  Show that the signal $x_n = A\cos(\omega n)$ can be fully predicted by a system with two weights $w_1,w_2$ (i.e. $x_n = w_1 x_{n-1} + w_2 x_{n-2}$). Find $w_1,w_2$.


Some ideas came up but, even if they are right, I can't seem to order them in the right direction:


I can see that $x'' = -\omega^2x$. Does it connected somehow to what is asked?
I guess it has something to do with stationary signals. If yes, how can I prove that this signal is stationary? (Also, somehow I can't find in the internet a clear definition of "stationary signal". Just vague ideas like "not dependant on time". What does this mean mathematically for a signal to be "not dependant on time"?)
Maybe it is concerned with some trigonometry of this form:
\begin{align} x_{n+2} &amp;= A\cos((n+2)\omega) \\ &amp;= A\cos(n\omega + 2\omega) \\ &amp;= A\cos(n\omega)\cos(2\omega) - A\sin(n\omega)\sin(2\omega) \\ &amp;= B\cos(n\omega) + C\sin(n\omega)\end{align}
I could go on with this development but I am realy not sure what am I looking for..


Any help?
Thanks!
HINT:

Use

$$2\cos(x)\cos(y)=\cos(x+y)+\cos(x-y)$$

with $x=(n-1)\omega$ and $y=\omega$.