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三角消去法是指从一串含三角函数的条件等式中,全部或部分地消去所含的三角函数,得到含有代数字母或含代数字母及部分三角函数的新的关系式的数学方法。它除了要用到代入消元法,等值代换法或四则(等式的加、减、乘、除)消去法外,还必须用到三角公式或某些技能技巧。三角中会迂到这一类问题,解析几何中也常见到这类问题。对中学生来说,作这样的练习对于培养自然记忆三角公式,提高灵活应用三角公式的能力,对于培养学生观察、分析,寻找规律的能力都是有益的。以下按三角恒等式分四个方面谈谈解这类题的思考方法。
The triangle elimination method is a mathematical method that eliminates the trigonometric function contained in a string of conditional equations containing a trigonometric function in whole or in part and obtains a new relational expression containing an algebraic alphabet or an algebraic alphabet and a partial trigonometric function. In addition to substituting the elimination method, equal substitution method, or four equations (adding, subtracting, multiplying, dividing, etc.) to eliminate the law, it must also use trigonometric formulas or some skill techniques. The triangle will encounter this type of problem, which is also commonly seen in analytical geometry. For middle school students, such exercises are beneficial for developing trigonometric formulas of natural memory, improving the ability to flexibly apply triangular formulas, and cultivating students’ ability to observe, analyze, and find laws. The following trigonometric identities are divided into four aspects to discuss ways of thinking about solving such problems.