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我们发现三角形中的两个优美的恒等式 .定理 1 在△ABC中 ,有tan(nA)tan[n(B -C) ]+tan(nB)tan[n(C -A) ]+tan(nC)tan[n(A -B) ]=-tan(nA)tan(nB)tan(nC)tan[n(A -B) ]tan[n(B -C) ]tan[n(C -A) ],其中
We find two beautiful identities in triangles. Theorem 1 In △ABC, there are tan(nA)tan[n(B -C)]+tan(nB)tan[n(C -A)]+tan(nC ) tan[n(A - B)] = - tan(nA) tan(nB) tan(nC) tan[n(A - B)] tan[n(B - C)] tan[n(C - A) ],among them