Half Angle Formula of Cos Derivation

Now, we will prove the half angle formula for the cosine function. Using one of the above formulas of cos A,

cos A = 2 cos²(A/2) – 1

From this,

2 cos²(A/2) = 1 + cos A

cos² (A/2) = (1 + cos A) / 2

cos (A/2) = ±√[(1 + cos A) / 2]