Answer
$$1$$
Work Step by Step
\begin{align*}
\lim _{x \rightarrow 0} \frac{\sin (\sin x)}{x}&=\lim _{x \rightarrow 0} \frac{\sin (\sin x)}{\sin x} \cdot \frac{\sin x}{x}\\
&=\lim _{x \rightarrow 0} \frac{\sin (\sin x)}{\sin x} \cdot \lim _{x \rightarrow 0} \frac{\sin x}{x}\\
&=1 \cdot 1\\
&=1
\end{align*}