三角条件等式题涉及的知识面较广,解题技巧较高,是培养学生能力的一项重要内容。证三角条件等式的关键,在于抓住“条件”与“待证”之间的内在联系、结构特征,联想有关的基础知识,进行恰当的变换。虽无固定的解题模式,但也有规律可循。常用到的基本思考方法有如下几种: 一、消去法待证式中的字母少于已知条件中的字母个数时,一般可用消去法入手,从已知式中消去待证式中所没有的字母,再进行变换。例1 已知△ABC中,sinA、sinB、sinC成等差数列,求证:ctg(A/2)·ctg(C/2)=3 分析:已知条件是含A、B、C的关系式,而待式是含半角A、C的关系式,易知需消去B,并 The problems involved in the trigonometric equation equations are broader, and the problem-solving skills are relatively high. This is an important part of cultivating students’ abilities. The key to the conditional equation of the verification triangle is to grasp the intrinsic relationship between the “conditions” and the “certifications to be witnessed” and the structural characteristics, and associate the relevant basic knowledge with appropriate transformation. Although there is no fixed problem solving model, there are rules to follow. The basic thinking methods that are commonly used are as follows: 1. Eliminating the law When the letters in the proofs are less than the number of letters in the known conditions, it is generally possible to use the elimination method to eliminate the known types. No letter, then change. Example 1 It is known that in △ABC, sinA, sinB, and sinC are in the sequence of equal errors. Proof: ctg(A/2).ctg(C/2)=3 Analysis: The known condition is the relationship including A, B, and C. , and the formula is a relation with half angles A and C. It is easy to know that the B needs to be eliminated, and