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Homework Help: Quick simple indentity explanation needed

  1. Mar 9, 2009 #1
    1. The problem statement, all variables and given/known data
    When you have something like eq.gif

    and you wanna use the pythagorean's theorem identity but lets say i do it with the 3rd term in the parenthesis, then would this be valid

    and what about this eq.gif is this also valid?

    2. Relevant equations


    3. The attempt at a solution

  2. jcsd
  3. Mar 9, 2009 #2
    no it would not be valid.

    to verify this, cube and square sin(x)^2 + cos(x)^2 = 1, and check
  4. Mar 13, 2009 #3
    Heh, my students just learned proving identities, and they've been kicking them in the ***...
    [tex]sin^{5}x cos^{2}x = (cos^{2}x - 2cos^{4}x + cos^{6}x)sin x[/tex]
    You do want to use the Pythagorean identity, but not in the first step. You can also start on either side, but I did from the left.

    If you start from the left side, my hint would be to rewrite [tex]sin^{5}x cos^{2}x[/tex] using the properties of exponents so that it equals (everything else) times sin x.

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