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在三角的求值或证明问题里,我们经常要根据解决问题的需要,把一个角的表示式变换成与它完全相等的几个角的代数和的形式,这就是三角变换中的一个基本方法——变角法。它与代数里因式分解的拆项、凑项有类似之处,都对问题的巧妙解决起着极其重要的作用。本文就变角法的几个应用简单地作些介绍: 一、用来求值。例1 求tg9°+ctg117°-tg243°--ctg351°的值。(1982年高考文科试题) 解原式=tg9°-tg27°-tg63°+tg81°=(tg9°+tg81°)-(tg27°+tg63°)
In the problem of evaluation or proof of a triangle, we often need to transform the expression of an angle into an algebraic sum of several angles that are exactly equal to it, which is a basic method in the triangular transformation. - Angle change method. It has similarities with algebraically decomposed disassembly and complications, and plays an extremely important role in the clever solution of the problem. This article briefly describes some applications of the angle change method: First, it is used to evaluate. Example 1 Find the value of tg9°+ctg117°-tg243°--ctg351°. (1982 entrance examination liberal arts test questions) solution original = tg9 ° -tg27 ° -tg63 ° +tg81 ° = (tg9 ° +tg81 °) - (tg27 ° +tg63 °)