由正弦定理,b/c = sinB/sinC = cosB/cosC,得:sinBcosC - cosBsinC =0 ,
即:sin(B-C) =0 ,所以 B=C,b=c;
因 a= c/2 ,b=c,代入余弦定理:cosA = (b²+c²-a²)/2bc = (c²+c² - c²/4)/2c² = 7/8 .
由正弦定理,b/c = sinB/sinC = cosB/cosC,得:sinBcosC - cosBsinC =0 ,
即:sin(B-C) =0 ,所以 B=C,b=c;
因 a= c/2 ,b=c,代入余弦定理:cosA = (b²+c²-a²)/2bc = (c²+c² - c²/4)/2c² = 7/8 .