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

[BrendanM]

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 doesn't make sense to me. please help

 

[Tide]

Hint: The slope of a straight line is the angle the line makes with the x-axis.

 

[HallsofIvy]

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?

 

[courtrigrad]

HallsofIvy is correct. The slope of a line is the tangent of its inclination.

 

[Tide]

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