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Homework Help: Trigonometry identities

  1. Apr 25, 2010 #1
    1. sec^4 x + sec^2 x tan^2 x - 2 tan^4 x = ?
    The possible answers are:
    a. 4 sec^2 x
    b. 3 sec^2 x - 2
    c. sec^2 x + 2
    d. tan^2 x - 1



    2. Relevant equations

    No idea.

    3. The attempt at a solution

    I'm not sure where to begin here. My book first doesn't cover anything above squared, and when it does, the equation is by itself and immediately shows an easy way to convert to simpler terms. I'm confused however on how to convert this equation.

    does sec^4 x = 1/cos^4 x?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 25, 2010 #2
    Yes, sec^4 x is 1/cos^4 x. Try converting everything in the expression to sines and cosines.
     
  4. Apr 25, 2010 #3
    okay, so is this correct?

    1/cos^4 x + 1/cos^2 x * sin^2 x/cos^2 x - 2(sin^4 x/cos^4 x)
     
  5. Apr 25, 2010 #4
    Yes. Now factorize out [tex]\frac 1{cos^4x}[/tex] and factorize the terms containing [tex]sin^2x[/tex]. Now, you should be able to apply well known identities to get a numerator that only contains terms involving [tex]cos^2x[/tex]. Now, it should be clear what the answer is.
     
  6. Apr 25, 2010 #5
    Yes, now simplify that.
     
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