文[1]介绍了有关不等式的两个引理及其推广命题1—4.文[2]将两个引理及其推广命题作出了进一步推广.本文将推广的两个引理及其推广的命题再进一步作出拓广.两个引理的再拓广如下:引理1设α,β均为锐角,n,m∈N+,则1sinnm2α+1sinnm2β≥2sinnm(α+β)(1)当且仅当α=β时取等号. In [1], we introduce two lemmas related to inequalities and their generalization propositions 1-4. [2] further promote the two lemmas and their extension propositions. The two lemmas that will be generalized in this paper and their generalization The proposition is further broadened. The extension of the two lemmas is as follows: Lemma 1 Let α and β be acute angles, n, m∈N+, then 1sinnm2α+1sinnm2β≥2sinnm(α+β) (1) When And only when α = β equal sign.