GS. 3 Given that $\cos \alpha=-\frac{99}{101}$ and $180^{\circ}<\alpha<270^{\circ}$. Find the value of $\cot \alpha$.
$\begin{array}{l}\sec \alpha=-\frac{101}{99} \\ \tan ^{2} \alpha=\sec ^{2} \alpha-1 \\ =\left(-\frac{101}{99}\right)^{2}-1 \\ =\frac{101^{2}-99^{2}}{99^{2}} \\ =\frac{(101-99) \cdot(101+99)}{99^{2}} \\ =\frac{400}{99^{2}} \\ \tan \alpha=\frac{20}{99} \\ \cot \alpha=\frac{99}{20} \quad(=4.95) \\\end{array}$