本文就二角函数值的求解问题中的两个增解问题进行分析与讨论．例1已知sinα-sinβ=-2/3①cosα-cosβ=2/3②且α,β∈(0,π/2),试求tan(α-β)的值,错解由①~2+②~2并整理得cos(α-β)=5/9．又∵α,β∈(0,π/2),∴-π/2＜α-β＜π/2．∴sin(α-β)=±(1-(5/9)~2)~(1/2) =±(2(14)~(1/2))/9,∴tan(α-β)=±(2(14)~(1/2))/5．分析以上解题过程似乎推理严谨,无懈可击,但只要细致观察则可发现：条件sinα- sinβ=-2/3中隐含了“α＜β”。增解忽略了α＜β This paper analyzes and discusses two solutions to the problem of solving the function of the two-corner function. Example 1 It is known that sinα-sinβ=-2/31cosα-cosβ=2/32 and α,β∈(0,π/2), try to find the value of tan(α-β), and the solution is from 1 to 2+2. ~2 and sort out cos(α-β)=5/9. Also ∵α,β∈(0,π/2),∴-π/2<α-β<π/2. ∴sin(α-β)=±(1-(5/9)~2)~(1/2) =±(2(14)~(1/2))/9, ∴tan(α-β) =±(2(14)~(1/2))/5. The analysis of the above problem-solving process seems to be rigorous and infallible, but as long as careful observation can be found: the condition sinα-sinβ=-2/3 implies “α <β”. Resolution ignores α<β