if theta is the angle between unit vectors A bar and B bar, then (1-A bar.B bar)/(1 plus A bar.B bar) is equal to

Define u=A.B=ABcosTheta

the problem then is

(1-u)/(1+u)=(1-u)^2/(1-u^2)

To solve this, we'll need to use the dot product of vectors.

The dot product of two vectors A and B is defined as the product of their magnitudes and the cosine of the angle between them:

A · B = |A| |B| cos(theta)

Given that A and B are unit vectors (|A| = |B| = 1), the dot product simplifies to:

A · B = cos(theta)

Substituting this into the expression (1 - A · B) / (1 + A · B), we get:

(1 - cos(theta)) / (1 + cos(theta))

This is the final expression for (1 - A · B) / (1 + A · B) when theta is the angle between unit vectors A and B.