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

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