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Homework Help: Trignometric identities question

  1. Jan 31, 2005 #1
    Hi,

    the question is

    2sin^2 + sinX -1 = 0

    I think the next step is then

    2(1-cos^2)+cos^2=0

    Did I do something wrong because I cannot seem to continue the question?
     
  2. jcsd
  3. Jan 31, 2005 #2
    Just replace sin(x) by a variable p.
    the equations then is 2p² + p - 1 = 0

    Solve this equation for p and then set these solutions equal to sin(x)
    At best you will have two goniometric equations to solve

    marlon
     
  4. Jan 31, 2005 #3

    dextercioby

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    Yes,i've colored in red what is wrong,namely
    [tex] \sin x -1=\cos^{2} x [/tex]

    That is wrong...As an indentity.It is valid as an equation in "x",which,i'm afraid,is not really equivalent to your initial one...

    Daniel.
     
  5. Jan 31, 2005 #4
    I still dont really understand...

    I tried it marlon's way

    2p^2+p-1=0
    2p^2+p=1
    2p+p=1 (squareroot)
    3p=1
    p=1/3

    Is the right?
     
  6. Jan 31, 2005 #5
    Not at all.

    Can you solve an equation like ax² + bx + c = 0 ?
    Discriminant D = b² -4ac

    first solution = [tex]\frac{-b + \sqrt{D}}{2a}[/tex]
    second solution = [tex]\frac{-b - \sqrt{D}}{2a}[/tex]

    Just apply this to your equation where x is now p

    marlon
     
  7. Jan 31, 2005 #6

    HallsofIvy

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    No, it isn't.

    square root of 2p^2+ p is NOT 2p+ p!

    Can you factor 2p^2+ p- 1?
     
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