Explanation

From tanA + cotA = 2, write cotA = 1/tanA: tanA + 1/tanA = 2 gives (tanA − 1)² = 0, so tanA = 1 (valid for 0 < A < 90°). Then every power of tanA equals 1, and the sum tan²A + tan³A + … + tanⁿA has n − 1 terms (exponents 2 through n), each equal to 1. The sum is therefore n − 1. The answer is (C).