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!

Double Angle Formula

  1. Dec 1, 2016 #1
    1. The problem statement, all variables and given/known data
    Simplify cos^2 8x - sin^2x

    2. Relevant equations


    3. The attempt at a solution
    I thought it would be in the format of cos2x
    But I can't seem to figure it out I tried cos (4 * 2x)

    And I tried to change the sin^2x into 1-cos^2x and I could get any farther.

    Not sure how else to simplify.
     
  2. jcsd
  3. Dec 1, 2016 #2

    RUber

    User Avatar
    Homework Helper

    Try writing it as cos(2*4x), or let u = 4x and then do it with cos(2u).

    EDIT:
    Sorry, I rushed through reading your problem. What tools do you have other than the double angle formula? You might be able to write this as a difference of squares first, then apply some identities.

    Do you know what the result should look like? How do you know when it is simple enough?

    Thanks.
     
    Last edited: Dec 1, 2016
  4. Dec 1, 2016 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What, really, is meant by "simplify"?

    The original result is about as simple as it gets. If you try to express everything in terms of ##\cos(x)## and ##\sin(x)## alone, your expression ##\cos^2 (8x) - \sin^2 x## becomes
    $$ 1-\sin^2 x -64 \cos^2 x + 1344 \cos^4 x - 10752 \cos^6 x + 42240 \cos^8 x\\ - 90112 \cos^{10} x
    +106496 \cos^{12} x -65536 \cos^{14} x +16384 \cos^{16} x $$
    Would you say that expression is simpler than the original one?
     
  5. Dec 1, 2016 #4
    There is no solution unfortunately it was just a problem given:(
     
  6. Dec 1, 2016 #5
    Yeah first one is definetly simpler.
     
  7. Dec 2, 2016 #6
    I have done this problem before, In my book they wanted it to be
    ##\cos(9x)\cos(7x)##.
     
  8. Dec 4, 2016 #7

    lurflurf

    User Avatar
    Homework Helper

    use reduction identities
    $$\cos^2(8x)=\frac{1+\cos(16x)}{2}\\
    \sin^2(x)=\frac{1-\cos(2x)}{2}$$
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Double Angle Formula
  1. Double-angle Formulae (Replies: 3)

  2. Double-angle Formulae (Replies: 3)

Loading...