y=cos2x-2sinx=-2sinx^2-2sinx+1=-2(sinx+1/2)^2+3/2
-π/4≤x≤π/4→-√2/2≤sinx≤√2/2
∴当sinx=-1/2(x=-π/6)时,ymax=3/2
当sinx=√2/2(x=π/4)时,ymin=-√2