文[1]通过构造长方体,利用代换方法证明了一些代数和三角不等式,读后很受启发,构造与变更,实现了问题的转化,获得证明不等式的一种有效途径.笔者的持续思考是,对于这些不等式,能不能直来直去的给出更加简明的证明方法呢?经探究是可简化的,这只要进行适度的代数变形,利用均值不等式、柯西不等式以及放缩技巧,笔者从高中教材基础知识出发给出直接证法,作为一份课程资源,供读者学习时参考. Wen [1] proves some algebraic and trigonometric inequalities by means of the substitution method by constructing a cuboid, which is inspired, constructed and changed after reading, which realizes the transformation of the problem and obtains an effective way to prove the inequality.The author’s continuous thinking is For these inequalities, can not be straightforward to give a more concise proof of it? By exploring is simplified, as long as the appropriate algebraic deformation, the use of mean inequality, Cauchy inequality and scaling techniques, the author from the high school textbook basis Knowledge to give direct card law, as a course resource, for readers to learn reference.