9. If $\sec x+\tan x=\frac{22}{7}, \csc x+\cot x$ $=\frac{m}{n}$, where $\frac{m}{n}$ is a reduced fraction, find $m+n$.


$$
\begin{array}{l}
\text { 9. } \because \sec ^{2} x-\tan ^{2} x=1 \text {, let } p=\frac{22}{7}, \\
\therefore \sec x-\tan x=\frac{1}{p}, \sec x+\tan x=p .
\end{array}
$$

Adding these two equations, we get $2 \sec x=p+\frac{1}{p}$. Subtracting them, we get
$$
\begin{aligned}
2 \tan x & =p-\frac{1}{p} . \\
& \therefore \cos x=\frac{2 p}{p^{2}+1}, \sin x=\frac{p^{2}-1}{p^{2}+1} . \\
& \therefore \csc x+\cot x=\frac{p+1}{p-1}=\frac{2}{15} \\
& \text { then } m+n=29+15=44 .
\end{aligned}
$$