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Question

If the centroid of a triangle formed by the points (0,0), (cos θ,sin θ) and (sin θ,cos θ) lies on the line y=2x,then wirte the value of tan θ.

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Solution

Centroid of triangle formed by

(0,0),(cos θ,sin θ) and (sin θ,cos θ) is

=(x1+x2+x33,y1+y2+y33)

=(cosθ+sinθ3,sinθcosθ3)

It lies on line y=2x,so

sinθcosθ3=2cosθ+sinθ3

sinθcosθ=2cosθ+2sinθsinθsinθ3 cosθ tanθ=3


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