1989 AIME Problem 10

Past Contests AIME AIME - 1989
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1

Let a, b, c be the three sides of a triangle, and let \alpha, \beta, \gamma, respectively, be the angles opposite them. If a^{2}+b^{2}=1989 c^{2}, find

\frac{\cot \gamma}{\cot \alpha+\cot \beta}