8. If for any $\alpha, \beta$ satisfying $\alpha \pm \beta \neq k \cdot 360^{\circ}$, we have
$$
\begin{array}{l}
\frac{\sin \left(\alpha+30^{\circ}\right)+\sin \left(\beta-30^{\circ}\right)}{\cos \alpha-\cos \beta} \\
=m \cot \frac{\beta-\alpha}{2}+n,
\end{array}
$$

then the array $(m, n)=$ $\qquad$
$$
\begin{array}{l}
\text { 8. }(m, n)=\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) . \\
\text { The left side of equation (1) }=\frac{2 \sin \frac{\alpha+\beta}{2} \cdot \cos \frac{\alpha-\beta+60^{\circ}}{2}}{-2 \sin \frac{\alpha+\beta}{2} \cdot \sin \frac{\alpha-\beta}{2}} \\
=\frac{\sqrt{3}}{2} \cot \frac{\beta-\alpha}{2}+\frac{1}{2},
\end{array}
$$

Comparing with the right side of equation (1) gives $m=\frac{\sqrt{3}}{2}, n=\frac{1}{2}$.