1983年第17届苏联数学竞赛十年级的一道三角问题,题设简洁,思考角度非常丰富,经过数十年的积淀成为经典.文[1]指出文[2]中的证明错误并给出一个新的证明方法.现笔者从不同角度对此题进行剖析其变式并加以推广.1题目已知α,β∈(0,π/2),且sin~2α+sin~2β=sin(α+β),求证α+β=π/2. A triangulation problem in the 10th year of the 1983 17th Soviet Mathematical Contest was concise and the angle of thought was very rich. After decades of accumulation, it became a classic. The article [1] pointed out that the proof error in [2] and gave a A new method of proof. Now the author analyzes this variant from different perspectives and generalizes it. 1 The topic is known as α,β∈(0,π/2), and sin~2α+sin~2β=sin(α +β) to verify α+β=π/2.