笔者在研究过程中发现很多问题都是围绕x2+y2=1和x2+y2=2(其中x,y∈Q)的结构来命制的,本文根据如下的两个三角恒等式,给出此类结构的一个经典构造.我们先来熟悉下两个三角恒等式:恒等式1:sin2θ+cos2θ=1;恒等式2:(sinθ+cosθ)2+(sinθ-cosθ)2=2;根据这两个三角恒等式,结合勾股数,我们很容易得出下面的两个恒等式. In the course of the research, I find that many problems are all about the structure of x2 + y2 = 1 and x2 + y2 = 2 (where x, y∈Q). According to the following two trigonometric identities, A classical structure of the structure. Let us first familiar with the next two trigonometric identities: Identity 1: sin2θ + cos2θ = 1; Identity 2: (sinθ + cosθ) 2+ (sinθ-cosθ) 2 = 2; According to these two trigonometric identities , Combined with the Pythagorean number, we can easily draw the following two identities.