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Homework Help: 1 - tan(theta)

  1. Jun 5, 2013 #1
    This problem is:

    [itex]\frac{sin(45)cos(\theta) - cos(45)sin(\theta)}{x} = 1 - tan(\theta)[/itex]

    I've been trying to find x mostly just by multiplying things by 1-tan(theta), but so far nothing I've tried yields the numerator.

    Also, [itex]sin(45)cos(\theta) - cos(45)sin(\theta) = sin(45 - \theta)[/itex], it that helps...
  2. jcsd
  3. Jun 5, 2013 #2


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    If you are to solve for 'x' why can't you just cross-multiply by 'x' and then divide by '1-tanθ '?

    Do you need to simplify or something like that?
  4. Jun 5, 2013 #3


    Staff: Mentor

    Is your goal to solve for x? To reduce confusion, that's why we ask posters to use the template and enter the complete problem description.

    If you're trying to solve for x, start by multiplying both sides of the equation by x.
  5. Jun 5, 2013 #4


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    Note that ##\sin(45)\cos(\theta) - \cos(45)\sin(\theta) = \sin(45 - \theta)## and that ##\tan(45 - \theta) = \frac{1 - \tan\theta}{1 + \tan\theta}##.
  6. Jun 10, 2013 #5
    Wow, that seems really obvious to me now that you brought that up, haha. I'm having a pretty bad time doing the long division though... Check it out ->

    [itex] x = \frac{sin(45)cos(\theta) - cos(45)sin(\theta)}{-tan(\theta) + 1}[/itex]

    I'm doing the leading terms in polynomial long division and I end up with...


    Ignoring the sin(45) term, I'm getting [itex]\frac{cos(\theta)}{tan(\theta)}[/itex] = [itex]\frac{adjacent}{hypotenuse}[/itex] * [itex]\frac{adjacent}{opposite}[/itex] = [itex]\frac{adjacent^2}{hypotenuse*opposite}[/itex]

    The [itex]\frac{adjacent^2}{hypotenuse*opposite}[/itex] term means nothing to me and doesn't really help solve. It's pretty difficult to figure this one out.
  7. Jun 10, 2013 #6


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    Which is exactly why that approach won't help you in this problem.

    Take a look at Curious3141's post and see what you can do with that.
  8. Jun 11, 2013 #7
    Oh I gotcha... because [itex]\frac{sine(x)}{cosine(x)} = tan(x)[/itex]... So I can just divide by cos(45 - [itex]\theta[/itex]) to end up with tan(45 - [itex]\theta[/itex]) which is equal to [itex]\frac{1 - tan(\theta)}{1 + tan(\theta)}[/itex]

    Yeah that makes a sense, thanks everyone.
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