由正弦公式:sinA/a=sinB/b=sinC/c
sinAsinBcosC=sin^2C两边同时除以abc
sinAsinBcosC/abc=sin^2C/abc
sin^2C/c^2*cosC=sin^2C/abc
cosC=c^2/ab
cosC=(a^2+b^2-c^2)/(2ab)
整理移项得
(a^2+b^2)/c^2=3
cosC=c^2/ab=(a^2+b^2-2abcosC)/(ab)
移项整理得
cosC=3/(3b)+b/(3a)≧2*根号(3/(3b)+b/(3a))=2/3
所以sinC的最大值=(1-cos^2C)^0.5=(1-4/9)^0.5=三分之根号五
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同除以abc后不应该是这样吗
追答你的等式右边的C哪里去了
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我算了最后是sinc啊?!
我是不是又哪里错了