2012年3月,江苏省南通市高考数学模拟考试第12题:若a_1x≤sinx≤a_2x对任意的x∈[0,π/2]都成立,则a_2-a_1的最小值为_____.关于本题的解法,各个地方、各个学校、各位老师有着多种不同的解法,本文就几种典型的解法进行分析.解法一:分离参数因为x∈[0,π/2],当x=0时,a_1x≤sinx≤a_2x成立当;x≠0时,将a_1x≤sinx≤a_2x变形为a_1≤(sinx)/x March 2012, Nantong City, Jiangsu Province entrance exam math mock question 12: If a_1x≤sinx≤a_2x for any x∈ [0, π / 2] are established, then a_2-a_1 minimum is _____. Solution of this problem, various places, all schools, teachers have a variety of different solutions, this article on the analysis of several typical solutions. Solution one: separation parameters because x ∈ [0, π / 2], when x = 0 , a_1x≤sinx≤a_2x holds; when x ≠ 0, a_1x≤sinx≤a_2x is transformed into a_1≤ (sinx) / x