angle between straight lines

Hi folks,

I am trying to show that the angle between two straight lines is given by:

I am using vector methods but my problem is the algebra. If the vector equation of a line is given by . And the second line by subscript 2, the angle between the lines is given by:

for a straight line of the form y = mx + c we have:

or,

So, the angle between the two lines is given by

At this stage I decided to square both sides and look for a chance to combine 1 and to give then simplify and take a square root to get back to

instead things got very messy indeed. Am I on the right track? I know it's murder trying to type lots of algebra but I suspect there would be less algebra if it was done right! A few lines in the right direction would be greatly appreciated!

best regards