If you stand on one leg you have to maintain your balance. If you wobble slightly you will move your other leg outwards or to one side to counterbalance your body and thereby retain balance. These are the same principles with respect to the physics as the use of a snow leopard's tail when hunting.

Glorious snow leopard. Photo: Danny Sullivan

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I think that most people know the answer to the question in the title by now. But just to clarify, the answer is that they use their tail as a balancing aid. It acts as a counterbalance when their body is twisting and turning on a hunt. The snow leopard lives in a particularly precarious and dangerous environment where to fall may be fatal.