JEE Math Practice Question

If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha $$,where –1 $$ \le $$ x $$ \le $$ 1, – 2 $$ \le $$ y $$ \le $$ 2, x $$ \le $$ $${y \over 2}$$ , then for all x, y, 4x2 – 4xy cos $$\alpha $$ + y2 is equal to :

1. A.4 sin2 $$\alpha $$
2. B.2 sin2 $$\alpha $$
3. C.4 sin2 $$\alpha $$ - 2x2y2
4. D.4 cos2 $$\alpha $$ + 2x2y2