在△ABC中,熟知a≤b A≤B,又由正弦定理sinA/sinB=a/b,可得如下有用结论:定理 若α、β>0,且α+β<π,则 α≤β sinα≤sinβ,等号当且仅当α=β时成立. 应用这个简单的定理,可以简捷、巧妙地解证一些三角不等式和几何难题. 例1 已知正数α、β、a、b满足: α<β,α+β<π, In ABC, we know that a≤b A≤B, and from the sine theorem sinA/sinB=a/b, we can get the following useful conclusions: Theorem If α, β>0, and α+β<π, then α≤β Sinα ≤ sinβ, the equal sign holds if and only if α=β. Applying this simple theorem, we can simply and ingeniously solve some triangle inequalities and geometric problems. Example 1 It is known that positive numbers α, β, a, b satisfy: α<β, α+β<π,