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