本人在数学通报(1991年第11期)上发表一篇短文(见[1])证明了正弦定理与余弦定理是等价的,但在从正弦定理导出余弦定理时,用了一个条件,即△ABC的内角和为π。因此有些读者就问这个条件能否去掉,若不能去掉就不能说正弦定理与余弦定理是等价的。问题提得好。首先我们要明确什么叫命题的等价性?所谓命题等价 I published a short article in the Mathematics Bulletin (No. 11 of 1991) (see [1]) that the sine theorem and the cosine theorem are equivalent, but when deriving the cosine theorem from the sine theorem, a condition is used. The internal angle sum of ABC is π. Therefore, some readers ask whether this condition can be eliminated. If it cannot be removed, it cannot be said that the sine theorem and the cosine theorem are equivalent. The problem is good. First of all, we must clarify what is the equivalence of propositions. The so-called propositional equivalence