在解决有关的竞赛问题时,常借助于题目显现的某些结构特征,引入三角代换,将所给问题转化为含有角的问题,然后运用三角函数的变换和性质进行求解.三角代换法是一种实用有效的解题方法,同时具有技巧性强的特征.例1(2008年湖北省预赛试题)设数列{an}满足a1=12,an+1=1+an1-an(n≥1) In the process of solving the related race problems, we usually use some of the structural features that appear in the topic to introduce the trigonometric substitution to transform the problem into the problem with the angle, and then use the transformation and the nature of the trigonometric function to solve the problem. Is a practical and effective method of solving problems, at the same time has a strong technical characteristics.Example 1 (2008 Hubei province preliminaries test) set the number of columns {an} satisfy a1 = 12, an + 1 = 1 + an1-an 1)