已知△ABC中,sinA·(cosC/2)^2+sinC·(cosA/2)^2=3/2sinB,求证sinA+sinC=2sinB
问题描述：
已知△ABC中,sinA·(cosC/2)^2+sinC·(cosA/2)^2=3/2sinB,求证sinA+sinC=2sinB
答
sinA·cos²C/2+sinC·cos²A/2=3/2sinB∵cos²C/2=1/2(1+cosC), cos²A/2=1/2(1+cosA)∴sinA*1/2(1+cosC)+sinC*1/2(1+cosA)=3/2sinB∴sinA+sinAcosC+sinC+sinCcosA=3sinB∴sinA+sinC+(sinAcosC+cos...