At their point of intersection the angle 0 between any two n

At their point of intersection, the angle 0 between any two nonparallel lines satisfies the relationship:

(M₂ - M₁)cos 0 = sin 0 + M₁M₂sin 0

Where M₁ and M₂ represent the slopes of the two lines. Rewrite the equation in terms of a single trig function.

Solution

(M₂-M₁)cos theta=sin theta + M₁M₂sin theta

Dividing both sides by cos theta

M₂-M₁=tan theta +M₁M₂tan theta

tan theta= (M₂-M₁)/(1+M₁M₂)