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Differentiating the identity to develop another identity

  1. Jan 27, 2009 #1
    1. The problem statement, all variables and given/known data

    Differentiate the identity sin2x = 2sinxcosx to develop the identity for cos2x, in terms on sin x and cos x

    2. Relevant equations



    3. The attempt at a solution

    Im not sure where to start with this one. Should I find the derivative of both sides of the equation, and then where do I go from there? The right side of that equation is 2cos^2x + sin^2x but im not sure how I can use that.

    Your help is appreciated as always!
     
  2. jcsd
  3. Jan 27, 2009 #2
    I believe you differentiated the right-hand side incorrectly:

    [itex]\frac{d}{dx}(2\sin(x)\cos(x)) = 2(\cos^{2}(x) + (-\sin^{2}(x)))[/itex]


    [itex]\Rightarrow 2\cos(2x) = 2(\cos^{2}(x) - \sin^{2}(x))[/itex]


    [itex]\Rightarrow \cos(2x) = \cos^{2}(x) - \sin^{2}(x)[/itex]


    which is a well-known double-angle formula.
     
  4. Jan 27, 2009 #3
    Actually, once you find the dertivative of both sides, you will get the identity instantly(barring some cancellations).

    Find the derivative of the left and right side (what u have written is not correct), using product rule, and see what cancels, on both sides
     
  5. Jan 27, 2009 #4
    Thank you very much. I mistakenly used part of the quotient rule instead of the product rule, meaning I subtracted instead add added which caused me to get the + sin ^2x

    Cheers guys!
     
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