向量作为一种工具在解题中的应用极广,巧用公式a·b≤a·b解题,方法新颖、运算简捷.本文举例说明该公式的应用.1在求值中的应用例1若α,β∈(0,π),求满足等式cosα+cosβ-cos(α+β)=23的α,β的值.解原等式可化为(1-cosβ)cosα+sinβsinα=32-cosβ.构造向量a=(1-cosβ,sin Vector is used as a tool in solving problems. It is cleverly used to solve problems with the formula a·b≤a·b. The method is novel and the operation is simple. This paper illustrates the application of this formula. 1 The application in evaluation 1 If α,β∈(0,π), find the value of α,β that satisfies the equation cosα+cosβ-cos(α+β)=23. The original solution equation can be (1-cosβ)cosα+sinβsinα= 32-cosβ. Construct Vector a=(1-cosβ,sin