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22 April, 04:15

Prove the identity cos (x-y) - cos (x+y) = 2sinx siny

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  1. 22 April, 04:35
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    see explanation

    Step-by-step explanation:

    Using the Addition / Subtraction formulae for cosine

    Consider the left side

    cos (x - y) - cos (x + y)

    = cosxcosy + sinxsiny - (cosxcosy - sinxsiny) ← distribute

    = cosxcosy + sinxsiny - cosxcosy + sinxsiny ← collect like terms

    = 2sinxsiny = right side ⇒ proven
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