Let A be an acute angle such that \tan A=2 \cos A. Find the number of positive integers n less than or equal to 1000 such that \sec ^{n} A+\tan ^{n} A is a positive integer whose units digit is 9 .
Let A be an acute angle such that \tan A=2 \cos A. Find the number of positive integers n less than or equal to 1000 such that \sec ^{n} A+\tan ^{n} A is a positive integer whose units digit is 9 .