a triangle $ABC$with fixed base $BC$, the vertex $A$moves such that $\cos B+\cos C=4\frac{{\sin }^{2}A}{2}\dot{}$If $a,bandc,$denote the length of the sides of the triangle opposite to the angles $A,B,andC$, respectively, then$b+c=4a$ (b) $b+c=2a$the locus of point $A$is an ellipsethe locus of point $A$is a pair of straight lines

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