tanA*tanB/（tanA+tanB）=1004tanC得(sinAsinB)/(sinAcosB+sinBcosA)=1004sinC/cosC采用正弦定理(ab)/(acosB+bcosA)=1004c/cosC采用余弦定理化简得(ab)/c=1004c/[(a^2+b^2-c^2)/(2ab)]a^2+b^2-c^2=2008c^2a^2+b^2=2009c^2所以m=2009，选C
