三角形abc三边分别为a,b,c,且a^2+b^2=kc^2 若cotc/(cota+cotb)=1004,求k的值

cos C=(a^2+b^2-c^2)/2ab=(k-1)/2abcotC/(cotA+cotB)=cos C*sin A*sin B/[(sin Acos B+sin Bcos A)*sinC]=cos C*sin A* sin B/sin^2C=(k-1)/2ab*sin A*sin B/sin^2C=1004sin A/a=sin B/b=sin C/c=2R（k-1）/2=1004m=...