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I can't figure this Trig Identity out help please?

  1. Aug 8, 2012 #1
    I need to verify the given identity. I've tried every which way i can think of, but can't figure this one out. I am self-studying this book "College Trigonometry 5th Edition by Aufmann.

    This is exercise set 3.3, problem 63.

    cos^2(x) - 2sin^2(x)cos^2(x) - sin^2(x) + 2sin^4(x) = cos^2(2x)

    Can anyone figure this out, or is this a misprint?

    Thanks for your help,

    Joe
     
  2. jcsd
  3. Aug 8, 2012 #2
    Have you tried using the double angle formulae for cosine to expand the right hand side?
     
  4. Aug 8, 2012 #3

    uart

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    Science Advisor

    No Joe, it works out ok.

    Start with [itex]cos^2 x - sin^2 x = cos 2x[/itex] and square both sides. This gets you the require RHS straight up and most of the terms you require on the LHS too. You then need to do a bit more work (apply more trig identities to the terms that don't yet "fit") on the LHS and it comes out fairly easily.
     
  5. Aug 8, 2012 #4
    Thanks, uart, I finally figured it out. I was starting on the left side instead of the right. After factoring and factoring and factoring it finally worked out! I've never factored so much in my life!!!

    Joe
     
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