Answer
$$\lim\limits _{x \rightarrow \pi} \sin (x-\sin(x))=0
$$
The function is continuous at $ x=\pi $.
Work Step by Step
Given $$\lim\limits _{x \rightarrow \pi} \sin (x-\sin(x))
$$
Firstly,
\begin{aligned}a)\lim\limits _{x \rightarrow \pi} \sin (x-\sin(x))&= \sin (\pi-\sin(\pi))\\
&= \sin (\pi-0)\\
&=0\\
\end{aligned}
Since $$ f(x)=\sin (x-\sin(x))$$
$$ b) f(\pi)=\sin (\pi-0)=0$$
From (a), (b) since $\lim \limits_{x \rightarrow \pi} f(x)=f(\pi)=0,$ the function is continuous at $ x=\pi $.
