cos 2A has THREE forms: $cos^{2A}$ - $sin^{2A}$ = 2$cos^{2A}$ - 1 = 1 - 2$sin^{2A}$. The last two forms are used to derive half-angle formulas: cos^2$$\frac{A}{2} = $\frac{1 + cosA}{2}$ and sin^2$$\frac{A}{2} = $\frac{1 - cosA}{2}$. Choose the form based on what needs to be eliminated.