In a △ABC with fixed base BC, the vertex A moves such that cosB+cosC=4sin²A​/2 .If a,b and c denote

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In a triangle ABC, with fixed base BC, the vertex A moves such that cosB+cosC=4sin^2(a/2)?In a triangle ABC, with fixed base BC, the vertex A moves such that cosB+cosC=4sin^2(a/2)?
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Find locus of vertex A of triangle ABC if m(ab)^2 + n(AC)^2 = c^2 which is a constant.Find locus of vertex A of triangle ABC if m(ab)^2 + n(AC)^2 = c^2 which is a constant.