导读 在三角形ABC中,求证:S△ABC=a^2/2(cotB+cotC) 解:cotB+cotC=cosB/sinB+cosC/sinC =[sinCcosB+cosCsinB]/simBsinC =...
在三角形ABC中,求证:S△ABC=a^2/2(cotB+cotC) 解:cotB+cotC=cosB/sinB+cosC/sinC =[sinCcosB+cosCsinB]/simBsinC =sin(B+C)/sinBsinC =sinA/sinBsinC ∵a/sinA=b/sinB ∴ cotB+cotC=a/bsinC bsinC=a/(cotB+cotC) S△ABC=absinC/2= a^2/2(cotB+cotC)。