In the adjoining figure, AB is a diameter of the circle, CD is a chord parallel to AB, and AC intersects BD at E, with ∠AED=α. The ratio of the area of △CDE to that of △ABE is[asy]
size(200);
defaultpen(fontsize(10pt)+linewidth(.8pt));
pair A=(-1,0), B=(1,0), E=(0,-.4), C=(.6,-.8), D=(-.6,-.8), E=(0,-.8/(1.6));
draw(unitcircle);
draw(A--B--D--C--A);
draw(Arc(E,.2,155,205));
label("A",A,W);
label("B",B,C);
label("C",C,C);
label("D",D,W);
label("α",E-(.2,0),W);
label("E",E,N);[/asy]<spanclass=′latex−bold′>(A)</span>cosα<spanclass=′latex−bold′>(B)</span>sinα<spanclass=′latex−bold′>(C)</span>cos2α<spanclass=′latex−bold′>(D)</span>sin2α<spanclass=′latex−bold′>(E)</span>1−sinα