问题描述: 在三角形ABC中,若sinA=(sinB+sinC)/(cosB+cosC),则△ABC的形状为 1个回答 分类:数学 2014-10-19 问题解答: 我来补答 sin(B+C)=(sinB+sinC)/(cosB+cosC)(cosB+cosC)(sinBcosC+cosBsinC)=sinB+sinC展开得 sinBcosBcosC+sinC(cosB)^2+sinB(cosC)^2+sinCcosCcosB=sinB+sinCsinBcosBcosC+sinCcosCcosB=sinB[1-(cosC)^2]+sinC[1-(cosB)^2]cosBcosC(sinB+sinC)=sinB(sinC)^2+sinC(sinB)^2cosBcosC(sinB+sinC)=sinBsinC(sinB+sinC)cosBcosC=sinBsinCcosBcosC-sinBsinC=0cos(B+C)=0B+C=90直角三角形. 展开全文阅读