如果△ABC三内角满足sin^2A+sin^2B=5sin^2C,求证sinC≤3/5
问题描述：
如果△ABC三内角满足sin^2A+sin^2B=5sin^2C,求证sinC≤3/5
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答
由正弦定理：a^2+b^2=5c^2 (a,b,c是相应的边)
cosC=(a^2+b^2-c^2)/(2ab)=4/5*(a^2+b^2)/(2ab)>=4/5
=> sinC