$$\begin{align} 2 \cos A \cos B &= \cos(A-B) \;+\; \cos(A+B) \\ 2 \sin A \;\sin B &= \cos(A-B) \;-\; \cos(A+B) \end{align}$$
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Proof without words: Pi from Square(root)s
$$ \huge \sqrt{2} + \sqrt{3} \;\approx\; \pi $$ $$\large \begin{align} \sqrt{2} + \sqrt{3} &= |\overline{AB}| + |\overline{CD}| \\ &= |\widehat{AB^\prime}| + |\widehat{CD^\prime}| \\ &\approx |\stackrel{\frown}{AB^\prime}| + |\stackrel{\frown}{CD^\prime}| \\ &\approx |\stackrel{\frown}{AC}| \\[6pt] &= \pi \end{align}$$
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