JEE Math Practice Question

If $$0 < \theta ,\phi < {\pi \over 2},x = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta } ,y = \sum\limits_{n = 0}^\infty {{{\sin }^{2n}}\phi } $$ and $$z = \sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\theta .{{\sin }^{2n}}\phi } $$ then :

1. A.xy $$-$$ z = (x + y)z
2. B.xyz = 4
3. C.xy + z = (x + y)z
4. D.xy + yz + zx = z