y=cos^2x-cosx+2=(cosx-1/2)^2+7/4cosx属于[-1,1],当cosx从1/2 -> 1时,y单调增cosx从1/2 -> -1时,y单调增当cosx从-1 -> 1/2时,y单调减cosx从1 -> 1/2时,y单调减再根据y是周期函数(周期是2π),可知,其单调增区间是[5π/3+2kπ, 2π+2kπ], [π/3+2kπ, π+2kπ]单调减区间是[π+2kπ, 5π/3+2kπ], [2kπ, π/3+2kπ]