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

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