If sin α = 4 / 5, Tan (α + β) = 1 and α is the second quadrant angle, then Tan β=

If sin α = 4 / 5, Tan (α + β) = 1 and α is the second quadrant angle, then Tan β=

∵ sin α = 4 / 5, α is the second quadrant angle ∵ cos α = - √ (1-sin & sup2; α) = - 3 / 5 ∵ Tan α = sin α / cos α = (4 / 5) / (- 3 / 5) = - 4 / 3 and Tan (α + β) = 1, so tan β = Tan [(α + β) - α] = [Tan (α + β) - Tan α] / [1 + Tan (α + β) * Tan α] (using tangent angle formula) = [1 - (- 4 / 3)

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