Trigonometric EquationHard
Question
In a triangle ABC with fixed base BC, the vertex A moves such that cosB + cosC = 4sin2 
. If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then
. If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, thenOptions
A.b + c = 4a
B.b + c = 2a
C.locus of point A is an ellipse
D.locus of point A is a pair of straight lines
Solution
2 cos
cos 
= 4 sin2 
cos = 2 sin (A/2)
⇒
⇒
⇒ b + c = 2a (constant).
cos = 4 sin2 cos
= 2 sin (A/2)⇒
⇒
⇒ b + c = 2a (constant).
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