# If the centroid of a triangle formed by the points (0, 0), (cos θ, sin θ) and (sinθ, - cosθ) lies on the line y = 2x, then write the value of tanθ.

Given:

The points (0, 0), (cos θ, sin θ) and (sinθ, - cosθ) lies on the line y = 2x

To find:

The value of tanθ.

Explanation:

The centroid of a triangle with vertices (x1,y1), (x2, y2) and (x3, y3)is given below:

Therefore, the centre of the triangle having vertices (0, 0,), (cos θ, sin θ) and (sin θ, cos θ) is

This point lies on the line y = 2x.

sinθ – cosθ = 2cosθ + 2sinθ

tanθ = -3

tanθ = 3

Hence, tanθ = 3

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