sinA+sinB+sinc=0 cosA+cosB+cosC=0 cos(B-C)

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sinA+sinB+sinc=0cosA+cosB+cosC=0cos(B-C)sinA+sinB+sinc=0cosA+cosB+cosC=0cos(B-C)sinA+sinB+sinc=0cosA

sinA+sinB+sinc=0 cosA+cosB+cosC=0 cos(B-C)
sinA+sinB+sinc=0 cosA+cosB+cosC=0 cos(B-C)

sinA+sinB+sinc=0 cosA+cosB+cosC=0 cos(B-C)
cos(B-C)=cosBcosC+sinBsinc又sinB+sinc=-sinA cosB+cosC=-cosA
所以同时平方sinB^2+sinc^2+2sinBsinc=sinA^2 cosB^2+cosc^2+2cosBcosC=cosA^2 两式相加 2(cosBcosC+sinBsinc)+2=1
cos(B-C)=cosBcosC+sinBsinc=-1/2

两个式子平方后相加即可