f(x)＝sin2x-2sin²x＝sin2x+(1-2sin²x)-1＝sin2x+cos2x-1＝√2sin(2x+π/4)-1.(1)最小正周期T＝2π/2＝π.(2)sin(2x+π/4)∈[-1,1],∴sin(2x+π/4)＝1时,所求最大值为：f(x)|max＝√2-1;sin(2x+π/4)＝-1...