在△ABC满足,sinA=(sinB+sinC)/(cosB+cosC),此三角形的形状是?

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在△ABC满足,sinA=(sinB+sinC)/(cosB+cosC),此三角形的形状是?
在△ABC满足,sinA=(sinB+sinC)/(cosB+cosC),此三角形的形状是?

在△ABC满足,sinA=(sinB+sinC)/(cosB+cosC),此三角形的形状是?
sinA=(sinB+sinC)/(cosB+cosC)
sin(B+C)=(sinB+sinC)/(cosB+cosC)
sinBcosC+cosBsinC=(sinB+sinC)/(cosB+cosC)
sinBcosBcosC+sinB(cosC)^2+(cosB)^2sinC+cosBsinCcosC=sinB+sinC
sinBcosBcosC+cosBsinCcosC=sinB-sinB(cosC)^2+sinC-(cosB)^2sinC
sinBcosBcosC+cosBsinCcosC=sinB(sinC)^2+(sinB)^2sinC
cosBcosC(sinB+sinC)=sinBsinC(sinB+sinC)
(cosBcosC-sinBsinC)(sinB+sinC)=0
cos(B+C)(sinB+sinC)=0
sinB+sinC≠0
所以cos(B+C)=0
B+C=90度,直角三角形