Problem

In a

\Delta 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 + c = 2a

c. locus of point

A

is an ellipse d. locus of point

A

is a pair of straight line