In a triangle ABC with fixed base BC,
the vertex A moves such that cos B +
cos C = 4 sin^2 (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
(1) b + c = 4a
(2) b + c = 2a
(3) Locus of point A is an ellipse
(4) Locus of point A is a pair of straight
lines
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