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Trig Identities

  1. May 21, 2009 #1
    ok ... heres my problem
    i need to prove that the LHS = RHS


    sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

    i tried to use the pythagarean identies and substitute the 1 and 2
    but tht isnt getting me anywhere .. plz help
     
  2. jcsd
  3. May 21, 2009 #2

    Cyosis

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    If you don't list the arguments of the functions we can't help you, also show the steps you've taken so far.
     
  4. May 21, 2009 #3
    ummm ok .. here's what i got


    sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

    LHS :

    = sin^2 + cos + cos - sin^2 - cos^2 / 1 + sin^2 + cos^2 + cos - cos^2
    ... here i cancelled the "sin^2" and " - sin^2" on the top and in the bottom i cancelled the "cos^2" and " - cos^2"

    = cos + cos - (cos)(cos) / 1 + sin^2 + cos

    = cos + cos - cos^2 / sin^2 + cos^2 + sin^2 + cos

    = cos + cos / sin^2 + sin^2 + cos

    ...... I dont noe what to do from here ... am i even tackling this problem the right way ??

    RHS :

    1 / 1 + sec

    = 1 / 1 + 1/cos
    = 1 + cos .... no problems here .. jus the LHS
     
  5. May 21, 2009 #4

    Cyosis

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    You forgot the arguments. Sin does not exist, sin(x) does etc.
     
  6. May 21, 2009 #5
    there all sin(x) or cos(x) :tongue2:
     
  7. May 21, 2009 #6

    Cyosis

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    Okay then we're arriving at the next problem. I have a feeling that some brackets are missing, for example what is 1/1+sec(x) is it [tex]1+\sec(x)[/tex] or [tex]\frac{1}{1+\sec x}[/tex]. Same goes for the right hand side. Use brackets to make divisions clear.
     
  8. May 21, 2009 #7
    itz

    [tex]\frac{1}{1+\sec x}[/tex]
     
  9. May 21, 2009 #8

    Cyosis

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    Yes, but what about the other side, similar ambiguities exist there. For me to assist you on this problem you will need to take all those ambiguities away.
     
  10. May 22, 2009 #9

    Mark44

    Staff: Mentor

    Are you trying to prove that
    [tex]sin^2(x) + 2cos(x) - \frac{1}{2} + cos(x) - cos^2(x) = \frac{1}{1 + sec(x)}?[/tex]

    That's actually the most reasonable way to interpret what you have written. (You've already told us what you meant on the right-hand side.
     
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