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Math Help - sinusoidal differentiation

  1. #1
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    sinusoidal differentiation

    Please help to solve this: y=cos^2x - sin^2x

    I don't know how to differentiate it. Thanks.
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  2. #2
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    Re: sinusoidal differentiation

    Assuming that the function is y =cos^2(x)-sin^2(x)

    y= y(cos^2(x))-y(sin^2(x))
    y= 2cosx(-sinx)- 2sinx(cosx)
    y= -2sinxcosx-2sinxcosx
    y= -4sinxcosx


    frank
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  3. #3
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    Re: sinusoidal differentiation

    thanks for replying. However, the back of the book has a different answer: -2sin2x

    could you clarify? Thanks
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  4. #4
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    Re: sinusoidal differentiation

    Thats because sin2x = 2sinxcosx (by double angle trigonometric identity)
    then
    -2sin2x = -2(2sinxcosx) = -4sinxcosx, and thats all.
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  5. #5
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    Re: sinusoidal differentiation

    thanks
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