Half angle formulas can be derived from the double angle formulas, particularly, the cosine of double angle. For easy reference, the cosines of double angle are listed below:
cos 2θ = 1 - 2sin2 θ → Equation (1)
cos 2θ = 2cos2 θ - 1 → Equation (2)
Note that the equations above are identities, meaning, the equations are true for any value of the variable θ. The key on the derivation is to substitute θ with ½ θ.