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The Taylor series expansion of $\frac{\sin x}{x-\pi}$ at $x=\pi$ is given by

1. $1+\frac{(x-\pi)^{2}}{3 !}+\ldots$
2. $-1-\frac{(x-\pi)^{2}}{3 !}+\ldots$
3. $1-\frac{(x-\pi)^{2}}{3 !}+\ldots$
4. $-1+\frac{(x-\pi)^{2}}{3 !}+\ldots$