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Product Identities (Product to Sum Identities)
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Product to sum identities are

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2 cosx cosy = cos (x + y) + cos(x - y)

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-2 sinx siny = cos (x + y) - cos(x - y)

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2 sinx cosy = sin (x + y) + sin(x - y)

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2 cosx siny = sin (x + y) - sin(x - y)