解由题知√2-2cosx＞0
即cosx＜√2/2
即2kπ+π/4＜x＜2kπ+7π/4 ,k属于Z
即函数y=lg(根号2-2cosx）的定义域
{x/2kπ+π/4＜x＜2kπ+7π/4 ,k属于Z}