Let, α, β ∈ (0, π / 2) and sin β = sin α cos (α + β), use the inequality a + B ≥ 2 √ AB (a > 0, b > 0) to find the maximum value of Tan β

Let, α, β ∈ (0, π / 2) and sin β = sin α cos (α + β), use the inequality a + B ≥ 2 √ AB (a > 0, b > 0) to find the maximum value of Tan β

Sin β = sin α cos (α + β) = 1 / 2 (sin (2 α + β) - sin β) = 1 / 2Sin (2 α + β) - 1 / 2Sin β, so 3 / 2Sin β = 1 / 2Sin (2 α + β), that is, 3sin β = sin (2 α + β) because 3sin β = sin (2 α + β) ≤ 1, that is, 3sin β ≤ 1 / 3 because β ∈ (0, π / 2), so sin β and Tan

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