In a \( \triangle A B C \) with fixed base \( B C \), the vertex \(...

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In a \( \triangle A B C \) with fixed base \( B C \), the vertex \( A \) moves such that \( \cos B+\cos C=4 \sin ^{2} \frac{A}{2} \).If \( a, b \) and \( c \) denote
P the lengths of the sides of the triangle opposite to the

W. angles \( A, B \) and \( C \) respectively, then
(2009)
(a) \( b+c=4 a \)
(b) \( b+c=2 a \)
(c) locus of point \( A \) is an ellipse
(d) locus of point \( A \) is a pair of straight line
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