在平面三角中有与代数中的平方差公式a~2-b~2=(a+b)(a-b)形似的恒等式: sin~2α-sin~2β=cos~2β-cos~2α=sin(α+β)·sin(α-β),(1)与 cos~2α-sin~2β=cos~2β-sin~2α=cos(α+β)·cos(α-β)。(2) 这两组恒等式不妨叫做三角中的“平方差”公式。熟记这两组恒等式对于解答某些三角问题、几何问题或综合题会有所帮助。恒等式(1)证明如下: ∵sin~2α-sin~2β=1/2(1-cos2α)-1/2(1-cos2β)=1/2(cos2β-cos2α)=sin(α+β)sin(α-β), In the plane triangle, there is an identity similar to the squared difference formula a~2-b~2=(a+b)(ab) in algebra: sin~2[alpha]-sin~2[beta]=cos~2[beta]-cos~2[alpha]=sin( α+β)·sin(α-β), (1) and cos~2α-sin~2β=cos~2β-sin~2α=cos(α+β)·cos(α-β). (2) These two sets of identities may be called the “squared difference” formula in the triangle. It is helpful to memorize these two sets of identities to solve certain triangular, geometric, or synthetic problems. Identity (1) is proved as follows: ∵sin~2α-sin~2β=1/2(1-cos2α)-1/2(1-cos2β)=1/2(cos2β-cos2α)=sin(α+β)sin (α-β),