Half Angle Formula of Sin Proof

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

cos A = 1 – 2 sin² (A/2)

From this,

2 sin² (A/2) = 1 – cos A

sin² (A/2) = (1 – cos A) / 2

sin (A/2) = ±√[(1 – cos A) / 2]