由余弦定理$${{a}^{2}}+{{b}^{2}}-2ab\cos \gamma ={{c}^{2}}$$，代入条件式得  $$2ab\cos \gamma =1988{{c}^{2}}$$，或$$\left( \frac{a}{b} \right)\left( \frac{b}{c} \right)\cos \gamma =994$$．  由下正弦定理$$\frac{a}{c}=\frac{\sin \alpha }{\sin \gamma }$$，$$\frac{b}{c}=\frac{\sin \beta }{\sin \gamma }$$，  于是$$\frac{\sin \alpha \sin \beta \cos \gamma }{{{\sin }^{2}}\gamma }=994$$．  因为$$\alpha +\beta +\gamma = \pi $$，所以$$\alpha +\beta = \pi -\gamma $$．从而$$\sin \left( \alpha +\beta \right)=\sin \gamma $$．  $$\frac{\cot \gamma }{\cot \alpha +\cot \beta }=\frac{\sin \alpha \sin \beta \cos \gamma }{\sin \left( \alpha +\beta \right)\sin \gamma }=994$$． 
设$$a$$，$$b$$，$$c$$是三角形的三边，$$\alpha $$，$$\beta $$，$$\gamma $$分别是相对于这三边的角，若$${{a}^{2}}+{{b}^{2}}=2021{{c}^{2}}$$，则$$\frac{\cot \gamma }{\cot \alpha +\cot \beta }=$$．

a) $\dfrac{1}{2021}$ 
b) $\dfrac{1}{1010}$ 
c) $1010$ 
d) $2021$ 