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Math Help - proving identities problem

  1. #1
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    proving identities problem

    cos(x+y)cos(x-y) = cos^2x - sin^2y
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  2. #2
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    Hello, reino17!

    Prove: . \cos(x+y)\cos(x-y) \;=\; \cos^2\!x - \sin^2\!y

    \cos(x+y)\cos(x-y) \;=\;(\cos x\cos y - \sin x\sin y)(\cos x\cos y + \sin x\sin y)

    . . . . . . . . . . . . . =\quad\;\;\cos^2\!x\cos^2\!y \quad - \quad \sin^2\!x\sin^2\!y

    . . . . . . . . . . . . . =\;\cos^2\!x\overbrace{(1 - \sin^2\!y)} - \overbrace{(1-\cos^2\!x)}\sin^2\!y

    . . . . . . . . . . . . . =\;\cos^2\!x - \cos^2\!x\sin^2\!y - \sin^2\!y + \cos^2\!x\sin^2\!y

    . . . . . . . . . . . . . = \qquad \cos^2\!x - \sin^2\!y

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  3. #3
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    this was really helpful. much thanks
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