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题 : 已知α、β为锐角 ,且ｓｉｎ(α +2 β) =2ｓｉｎα,求角α的最大值 ,并求此时ｔａｎ(α +β)的值。这是南充市 8所重点中学 ,高中 2 0 0 2级第一次联考第 1 9题 ,试题遵循了“能力立意、强调综合、重视数学思想和方法考查”的高考命题原则 ,是整套试卷的把关题之一。现
Problem: Know that α and β are acute angles, and sin(α +2 β) = 2sinα, find the maximum value of angle α, and find the value of tan(α + β) at this time. This is the 18th key secondary school in Nanchong City, the second year of the high school entrance examination for the second time in 2002. The questions follow the principle of “proficiency, emphasis on synthesis, and emphasis on mathematical thinking and method examination”, which is the entire examination paper. One of the questions. Now