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Let $f(x)=\frac{x}{1-\cos (x-2)}$.$\newline$Select the correct description of the one-sided limits of $f$ at $x=2$.$\newline$Choose $1$ answer:$\newline$(A) $\lim _{x \rightarrow 2^{+}} f(x)=+\infty$ and $\lim _{x \rightarrow 2^{-}} f(x)=+\infty$$\newline$(B) $\lim _{x \rightarrow 2^{+}} f(x)=+\infty$ and $\lim _{x \rightarrow 2^{-}} f(x)=-\infty$$\newline$(C) $\lim _{x \rightarrow 2^{+}} f(x)=-\infty$ and $\lim _{x \rightarrow 2^{-}} f(x)=+\infty$$\newline$(D) $\lim _{x \rightarrow 2^{+}} f(x)=-\infty$ and $\lim _{x \rightarrow 2^{-}} f(x)=-\infty$