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The mean, i.e., the expected value of $X_n$ is $$E\{X_n\}=E\{A\cos(\omega n)+B\sin(\omega n)\}\tag{1}$$ Since the expectation operator is linear, $(1)$ is equivalent to $$E\{X_n\}=E\{A\cos(\omega n)\}+E\{B\sin(\omega n)\}\tag{2}$$ and since $\cos(\omega n)$ and $\sin(\omega n)$ are deterministic you finally get E\{X_n\}=E\{A\}\cos(\omega n)+E\{B\}\sin(...