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三角换元法是一种用三角函数代替问题中的字母(或式子),然后利用三角函数之间的关系达到解题目的的一种解题方法.该解法的优点在于将已知条件通过代替转化为同一个角的某个三角函数来表示,从而利于我们运用熟知的三角公式进行化简,直至问题的解决.本文以部分数学高考题,自主招生试题,高中数学竞赛试题为例说明如下.例1(2012年浙江省高考题)若正数x、y满足x+3y=5xy,则3x+4y的最小值是
Triangulation method is a solution to the problem of using trigonometric functions instead of the letters (or formulas), and then using the relationship between the trigonometric functions to solve the problem.This method has the advantage that the known conditions are passed Instead of being transformed into the same corner of a trigonometric function to represent, so that we use the well-known triangular formula to simplify until the problem is solved.This paper takes part of the math entrance exam questions, high school mathematics competition questions as an example Example 1 (2012 Zhejiang Province Entrance Examination) If the positive number x, y satisfies x + 3y = 5xy, then the minimum value of 3x + 4y is