If α and β are complementary angles such that α - β = π/6 and m tan β = n tan α, then what is ((m+n)/(m-n)) equal to?

Since α + β = π/2, β = π/2 - α, so tan β = cot α. From m tan β = n tan α: m cot α = n tan α, so m/n = tan²α. Using componendo-dividendo: (m+n)/(m-n) = (tan²α + 1)/(tan²α - 1). With α - β = π/6 and α + β = π/2, we get α = π/3, β = π/6. tan²(π/3) = 3, so (3+1)/(3-1) = 4/2 = 2.