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Identity for tan(x-y) = [tan(x) - tan(y)]/[1-tan(x)tan(y)]

  1. Oct 19, 2004 #1
    Use the identity for tan(x-y) = [tan(x) - tan(y)]/[1-tan(x)tan(y)] to show that if two lines L1 and L2 intersect at angle theta then tan(theta) = m2-m1/(1 + m1m2) where m1 and m2 are the slopes of L1 and L2 respectivly.

    hmm ihave no idea where to start for this it doesnt make sense to me. plz help
     
  2. jcsd
  3. Oct 19, 2004 #2

    Tide

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    Hint: The slope of a straight line is the angle the line makes with the x-axis.
     
  4. Oct 20, 2004 #3

    HallsofIvy

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    No, the slope of a line is the TANGENT of the angle the line makes with the x-axis. Which is the whole point of this exercise!

    1) Draw a picture. You can always shift you coordinate system up or down, right or left without changing angles (or slopes) so draw it so that the two lines intersect at the origin. If the angles the two lines make with the x-axis are θ1 and θ2, what is the angle between them? What is the tangent of that angle?
     
  5. Oct 20, 2004 #4
    HallsofIvy is correct. The slope of a line is the tangent of its inclination.
     
  6. Oct 20, 2004 #5

    Tide

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    I knew that! Thanks for pointing out my typo! :-)
     
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