Topics · 3 identities

Product to Sum

Turning products of sines and cosines into sums.

sin · cos

sinαcosβ=12[sin(α+β)+sin(αβ)]\sin\alpha \cos\beta = \tfrac{1}{2}[\sin(\alpha+\beta) + \sin(\alpha-\beta)]
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cos · cos

cosαcosβ=12[cos(αβ)+cos(α+β)]\cos\alpha \cos\beta = \tfrac{1}{2}[\cos(\alpha-\beta) + \cos(\alpha+\beta)]
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sin · sin

sinαsinβ=12[cos(αβ)cos(α+β)]\sin\alpha \sin\beta = \tfrac{1}{2}[\cos(\alpha-\beta) - \cos(\alpha+\beta)]
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