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: 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,

  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


    User Avatar
    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!!!

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook