y=1-2sin²x-4sinx+1
=2-2sin²x-4sinx
令sinx=t,则y=-2t²-4t+2,t∈[-1,1]
开口向下,对称轴为t=-1,单调递减.
t=1时,ymin=-4
t=-1时,ymax=4
值域为[-4,4]