1991 AIME Problem 9

Suppose that \sec x+\tan x=\frac{22}7 and that \csc x+\cot x=\frac mn, where \frac mn is in lowest terms. Find m+n^{}_{}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.