$\begin{align}  & \underset{x\to 3}{\mathop{\lim }}\,f(x)=\underset{x\to 1}{\mathop{\lim }}\,f(x+2) \\  & \underset{x\to 3}{\mathop{\lim }}\,f(x)=\underset{x\to 1}{\mathop{\lim }}\,\frac{\cos \pi x}{1+\sin \pi x}=\frac{\cos \pi }{1+\sin \pi }=\frac{-1}{1+0}=-1 \\ \end{align}$