由倍角公式Cos2A=CosA^2-SinA^2=1-2SinA^2
COS2C=CosC^2-SinC^2=1-2SinC^2
代入4COS2A-COS2C=3得:
4(1-2SinA^2)-(1-2SinC^2 )=3
SinC^2= 4SinA^2
SinC=2SinA
由正弦定理知SinC/c=SinA/a
故c=SinC×a/SinA=2a
AB=c,BC=a=√5
AB=2BC=2√5
由倍角公式Cos2A=CosA^2-SinA^2=1-2SinA^2
COS2C=CosC^2-SinC^2=1-2SinC^2
代入4COS2A-COS2C=3得:
4(1-2SinA^2)-(1-2SinC^2 )=3
SinC^2= 4SinA^2
SinC=2SinA
由正弦定理知SinC/c=SinA/a
故c=SinC×a/SinA=2a
AB=c,BC=a=√5
AB=2BC=2√5