如果△ABC三内角满足sin^2A+sin^2B=5sin^2C,求证sinC≤3/5
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如果△ABC三内角满足sin^2A+sin^2B=5sin^2C,求证sinC≤3/5
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![如果△ABC三内角满足sin^2A+sin^2B=5sin^2C,求证sinC≤3/5](/uploads/image/z/6554603-11-3.jpg?t=%E5%A6%82%E6%9E%9C%E2%96%B3ABC%E4%B8%89%E5%86%85%E8%A7%92%E6%BB%A1%E8%B6%B3sin%5E2A%2Bsin%5E2B%3D5sin%5E2C%2C%E6%B1%82%E8%AF%81sinC%E2%89%A43%2F5)
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
cosC=(a^2+b^2-c^2)/(2ab)=4/5*(a^2+b^2)/(2ab)>=4/5
=> sinC
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