Trigonometric identity proof $\cos(A) + \cos( B)$ What is a nice proof of $$\cos(A) + \cos( B)= 2\cos\Big(\frac{A+B}{2}\Big)\cos\Big(\frac{A+B}{2}\Big)$$? 
I can prove it starting with the RHS but i want to be able to quickly prove it starting on the LHS as I won't have access to a formula book when I need it.

From LHS to RHS:
$$
\cos B + \cos A \\
\cos \frac {2 B} 2 + \cos \frac {2 A} 2 \\
\cos\left(\frac {A + B - A + B} 2 \right) + \cos\left(\frac {A + B + A - B} 2 \right) \\
\cos\left(\frac {A + B} 2 - \frac {A - B} 2 \right) + \cos\left(\frac {A + B} 2 + \dfrac {A - B} 2 \right) \\
\left[\cos\left(\frac{A + B} 2\right)\cos\left(\frac{A - B} 2 \right) + \sin\left(\frac{A + B} 2 \right)\sin\left(\frac{A - B} 2 \right)\right] + \left[\cos\left(\frac{A + B} 2 \right)\cos\left(\frac{A - B} 2 \right) - \sin\left(\frac{A + B} 2 \right)\sin\left(\frac{A - B} 2 \right)\right]\\
2 \cos\left(\frac {A + B} 2 \right) \cos\left(\frac {A - B} 2 \right) \\
$$
