What is (1 + cot α − cosec α)(1 + tan α + sec α) equal to?

Expanding: Let A = 1 + cot α − cosec α and B = 1 + tan α + sec α. Multiply: 1·1 + 1·tan α + 1·sec α + cot α·1 + cot α·tan α + cot α·sec α − cosec α·1 − cosec α·tan α − cosec α·sec α. Simplifying using cot α·tan α = 1 and grouping: this is a standard identity equal to 2.