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Trigonometric equation

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data
    [tex]tan(\alpha)=\sqrt{2}-1[/tex] for every alpha in ]0,90°[

    2. Relevant equations

    1-count tan(2α)

    2-conclude the value of α
    3. The attempt at a solution

    1-after using tan(2α)=(2tanα)/1-tan^2α) i got tan(2α)=(√2-1)/2

    2- I know that α is pi/8 but i just don't know how to conclude it.
     
  2. jcsd
  3. Feb 14, 2012 #2

    LCKurtz

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    Write that as$$\frac {\sqrt 2 - 1}{1}$$Then divide the numerator and denominator by ##\sqrt 2## and see if you recognize the result in form$$
    \frac{1-\cos\theta}{\sin\theta}$$ for some ##\theta##, and see if that formula rings any bells.
     
  4. Feb 14, 2012 #3

    Mark44

    Staff: Mentor

    The above should say, "for alpha in ]0,90°[".
    Your value for tan(2α) is incorrect. Show us how you got that value, and we'll help you get the right value.
     
  5. Feb 14, 2012 #4
    if i write it like you said and i keep solving, it just brings me back to tanα=√2-1
     
  6. Feb 14, 2012 #5

    LCKurtz

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    Show me what you did when you wrote it that way. What ##\theta## works?
     
  7. Feb 14, 2012 #6

    Mark44

    Staff: Mentor

    It's much simpler if you follow their hint.
    I assume this means compute tan(2α). If you do this, you get a very simple value for tan(2α), which you can use to find α.
     
  8. Feb 14, 2012 #7
    yea i solved it tan(2α)=1 and to conclude the value of α i did tan(2σ)=tanpi/4+2kpi and i just solve it out and i get α=pi/8
     
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