∵b/a+a/b=4cosC∴(a²+b²)/(ab)=4cosC又，cosC=(a²+b²-c²)/(2ab)∴(a²+b²)/(ab)=2(a²+b²-c²)/(ab)∴a²+b²=2a²+2b²-2c²∴a²+b²=2c²∴(sin^2A+sin^2B)/sin^2C=（a²+b²）/c² = 2
