How can we derive the double angle formulas for sine and cosine from the unit circle definitions of these functions?

To derive the double angle formulas for sine and cosine from the unit circle definitions, consider a point (cos θ, sin θ) on the unit circle. Using angle addition formulas, sin(2θ) = 2sin(θ)cos(θ) and cos(2θ) = cos²(θ) – sin²(θ) are derived.