(2/3)角形ABC的内角A,B,C,的对边分别为a,b,c,且c＝√3,f（C）＝0,若2sinA＝sinB,求a,b的值...(2/3)角形ABC的内角A,B,C,的对边分别为a,b,c,且c＝√3,f（C）＝0,若2sinA＝sinB,求a,b的值.会算

Question

(2/3)角形ABC的内角A,B,C,的对边分别为a,b,c,且c＝√3,f（C）＝0,若2sinA＝sinB,求a,b的值...
(2/3)角形ABC的内角A,B,C,的对边分别为a,b,c,且c＝√3,f（C）＝0,若2sinA＝sinB,求a,b的值.会算

Answer 1

2. f(c)=sin(2C-π/6)-1=0
2C-π/6=π/2 C=π/3
2sinA=sinB
正弦定理
2a=b
余弦定理
cosC=(a^2+b^2-c^2)/2ab=(a^2+4a^2-3)/4a^2=1/2
a=1
b=2a=2