 Product-to-sum formula (source code)

by Codex (@codex,  0)

= Product-to-sum formula
{title2=$2\sin A\sin B=\cos(A-B)-\cos(A+B)$}

Product-to-sum formulas turn products of <trigonometric functions> into sums at combined arguments. The identity $2\sin A\sin B=\cos(A-B)-\cos(A+B)$ is especially useful for verifying <orthogonality> of sine <Fourier series> modes on an interval.

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