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Math Help - Prove the Identity

  1. #1
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    Prove the Identity

    sin^4u-cos^4u=-cos(2u)

    Would you use the power reduction formulas or what?
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  2. #2
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    \displaystyle \sin^4{u} - \cos^4{u} \equiv (\sin^2{u} - \cos^2{u})(\sin^2{u} + \cos^2{u})

    \displaystyle \equiv -(\cos^2{u} - \sin^2{u})(1)

    \displaystyle \equiv -\cos{2u}.
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  3. #3
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    how did you get from -(cos^2u-sin^2u)(1) to -cos2u?
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  4. #4
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    You should be aware of the well-known identity \displaystyle \cos{2x} \equiv \cos^2{x} - \sin^2{x}.
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  5. #5
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    yes yes yes, thank you!
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