a triangle `A B C`with fixed base `B C`, the vertex `A`moves such that `cosB+cosC=4sin^2A/2dot`If `a ,ba n dc ,`denote the length of the sides of the triangle opposite to the angles `A , B ,a n dC`, 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 linesA. b+c=4aB. b+c=2aC. the locus of point A is an ellipseD. the locus of point A is a pair of straight lines

a triangle `A B C`with fixed base `B C`, the vertex `A`moves such that

1.	a triangle `A B C`with fixed base `B C`, the vertex `A`moves such that `cosB+cosC=4sin^2A/2dot`If `a ,ba n dc ,`denote the length of the sides of the triangle opposite to the angles `A , B ,a n dC`, 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 linesA. b+c=4aB. b+c=2aC. the locus of point A is an ellipseD. the locus of point A is a pair of straight lines
Answer» Given `cos B+cos C=4 sin^(2).(A)/(2)` `or 2 cos((B+C)/(2))cos ((B-C)/(2))=4 sin^(2).(A)/(2)` or `cos.((B-C)/(2))=2sin.((A)/(2))` `or 2 sin.(B+C)/(2)cos.(B-C)/(2)=4 sin.(A)/(2)cos.(A)/(2)` or `sin B+sin C=2 sin A` or `b+c=2a` Thus, sum of two variable sides is constant . Hence the locus of vertex A is an ellipse with B and C as foci,

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