Addition and Subtraction Formulas for Sine and Cosine IV

Proof Without Words: The Product-to-Sum Identities

$2\cos\alpha\cos\beta=\cos (\alpha+\beta)+\cos (\alpha-\beta)\\ 2\sin\alpha\cos\beta=\sin (\alpha+\beta)+\sin (\alpha-\beta)$

Summary. We present a wordless proof of two basic trigonometric identities involving two angles, sine, and cosine.


  1. J. Molokach, , The College Mathematics Journal, MAA, May 2016 (47), n 3, 199


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