The formula of the angle between two straight lines in the plane?

The formula of the angle between two straight lines in the plane?

Let the slopes of two straight lines be K1 and K2 respectively
Angle θ = arctan | (k1-k2) / (1 + k1k2)|

How to deduce the formula of the angle between two straight lines is very urgent
Cos θ = (A1A2 + b1b2) / [√ (A1 ^ 2 + B1 ^ 2) * √ (A2 ^ 2 + B2 ^ 2)] is the derivation of this formula

According to the vector formula A. B = a module B module cos θ, a, B after a single vector length, the former refers to the product of two vectors
So cos θ = a.b/a module B module can be obtained
The orthogonal decomposition of vector a = (A1, B1) B = (A2, B2), which is the coordinate of vector
a.b=(a1,b1)(a2,b2)=a1a2+b1b2

What is the formula of the angle between two straight lines?

The slopes of two straight lines are expressed by K1 and K2 respectively, then the tangent of the angle X between two straight lines can be expressed by the following formula:
tanx=|(k2-k1)/[1+(k2)(k1)]|