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Homework Help: Verifying an Identity

  1. Jan 7, 2010 #1
    The problem statement, all variables and given/known data

    I'm supposed to verify this:
    [tex]\frac{cos(2x)-cos(4x)}{sin(2x)+sin(4x)}=tanx[/tex]

    The attempt at a solution

    I reworked it every way I could think of, but it just won't work. I got desperate so I plugged it into some site and it said it was not a real identity, so I now I'm thinking maybe my teacher had a typo or something.
     
  2. jcsd
  3. Jan 7, 2010 #2

    rock.freak667

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    look up the sum to product formulas for sine and cosine. They should help.
     
  4. Jan 7, 2010 #3
    I already know them, but I still can't figure it out.
     
  5. Jan 7, 2010 #4

    rock.freak667

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    Try applying them.
     
  6. Jan 7, 2010 #5
    If you don't want to help then don't comment please.
     
  7. Jan 7, 2010 #6

    rock.freak667

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    Am I correct to assume you did not apply them?
     
  8. Jan 7, 2010 #7
    No, you are not. Before I posted here I used the sum/dif identities, pythagorean identities, and double angle formulas. Everything I did resulted in a dead end.
     
  9. Jan 7, 2010 #8

    rock.freak667

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    Is it possible that you can post your work using the sum to product identities?
     
  10. Jan 7, 2010 #9

    ehild

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    You can factor out sin2x from the denominator. Resolve it further as 2 sinx cosx, and write the right side as sinx/cosx. Eliminate cosx (assuming it is not zero). Divide both sides by sinx, and rewrite 2(sinx)^2 as 1-cos(2x). You can see that the denominator is equal to the numerator.

    ehild
     
  11. Jan 8, 2010 #10

    vela

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    You didn't use the right ones then. You need the sum-to-product identities. If you use them, the answer pops out in like two lines.

    Look for identities for [tex]cos a - cos b[/tex] and [tex]sin a + sin b[/tex].

    If, in fact, you used those already and didn't get anywhere, post what you did because that's where the difficulty lies.
     
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