Question

已知tanα=1/3,tanβ=1/5,tanγ=3/11,α，β，γ均为锐角。求α，β，γ的值

问求α+β+γ的值

Answer 1

α，β，γ均为锐角
∴ 0 < α+β < π

tan(α+β) = (tanα + tanβ) / (1 - tanα·tanβ) = 4/7
∴ 0 < α+β < π/2
∴ 0 < α+β+γ < π

tan(α+β+γ) = (tan(α+β) + tanγ) / (1 - tan(α+β)·tanγ) = 1
∴ α+β+γ = π/4