I am highly confused about the stability of $\cos(x[n])$.
If we provide a bounded input such as $x[n]=u[n]$, the output is bounded.
Now if we provide an unbounded signal $x[n]=\delta[n]$, the output oscillates between $-1$ and $1$. So I think it's marginally stable in this case.
Am I correct? I have this confusion because in my book it says it's unstable when $x[n]=\delta[n]$. So my questions are: Is the function BIBO stable and also is it stable for an unbounded input ?
Note: $u[n]$ and $\delta[n]$ are unit step and dirac delta functions respectively.
Correction: As mentioned in the comment, $x[n]=\delta[n]$ is bounded too.
But this points more strongly to $\cos(x[n])$ being stable, isn't it?