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利用构造几何图形来求解或证明代数、三角中的问题,不少期刊对此法都作了介绍,但大多数都是通过构造三角形、矩形或正方形来解(证)的。那么,能否构造梯形作为几何模型呢?答案是肯定的。一、构造梯形证明定理、公式例1 证明两角和的正弦函数的加法公式:设α和β均为锐角,求证:sin(α+β)=sinαcosβ+cosαsinβ。证明:如图1,构造一个直角梯形ACDE,使α和β均为锐角,并且使BB=BD=1,易知AE=sinα,AB=cosα,CD=sinβ,BC=cosβ,而
Using structural geometry to solve or prove problems in algebra and triangles, many journals have introduced this method, but most of them are solved by constructing triangles, rectangles, or squares. So, can we construct a trapezoid as a geometric model? The answer is yes. First, the structure of the trapezoidal proof theorem, formula Example 1 prove the addition formula of the sine function of the two-angle sum: Let α and β be acute angles, verify: sin(α+β)=sinαcosβ+cosαsinβ. Proof: As shown in Figure 1, construct a right-angle trapezoid ACDE, make α and β are acute angles, and make BB = BD = 1, it is easy to know AE = sinα, AB = cosα, CD = sinβ, BC = cosβ, and