我国著名的数学家杨乐院士在函数值分布论的研究中曾建立如下的一个三角不等式 :cos2 λA+cos2 λB- 2 cosλAcosλBcosλπ≥sin2 λπ (1 )其中 A0 ,B0 ,A+B≤π,0 λ1 .此不等式有许多证法见文 [1 ]～ [3 ],文 [4]～ [6]对不等式 (1 )进行各种探索和推广 .如文 [4]一下 Academician Yang Le, a famous mathematician in China, has established a triangular inequality in the study of function value distribution theory: cos2 λA+cos2 λB-2 cosλAcosλBcosλπ≥sin2 λπ (1) where A0,B0,A+B≤π,0 Λ1. There are many proofs of this inequality, see [1] ~ [3], [4] ~ [6] for inequality (1) for a variety of exploration and promotion. As text [4]