$\frac{\cos 9°+\sin 9°}{\cos 9°-\sin 9°}$

$\begin{array}{l}\frac{\sin 81°+\sin 9°}{\sin 81°-\sin 9°}=\frac{2\sin \left(\frac{81°+9°}{2}\right)\cos \left(\frac{81°-9°}{2}\right)}{2\cos \left(\frac{81°+9°}{2}\right)\sin \left(\frac{81°-9°}{2}\right)}\\ =\frac{\sin 45°\cos 36°}{\cos 45°\sin 36°}\\ =\frac{\frac{1}{\sqrt{2}}\cos 36°}{\frac{1}{\sqrt{2}}\sin 36°}=\cot 36°\end{array}$