In a triangle ABC with fixed base BC, the vertex A moves such that
$$\cos B + \cos C = 4 \sin^2 \frac{A}{2}$$
If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then

A

$$b + c = 4a$$

B

$$b + c = 2a$$

C

locus of point A is an ellipse

D

locus of point A is a pair of straight lines