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17.参考答案解:(1)因为cos2B=cos(A C),所以2cos2B-1=-cosB,(2分)解得cosB=或cosB=-1(舍).(4分)由B为三角形的内角,得B=-.(5分)3(2)因为 asin A csin c=6sinB,所以由正弦定理,得a2 c2=6b=18.(6分)12 c2-9=9,所以a=9.(8分)因为cosB=2=-2ac2ac因为(a c)2=a2 c2 2ac=18 18=36,所以a c=6,(9分)所以△ABC的周长a b c=9.(10分)
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