1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook