How is Cos B expressed according to the Law of Cosines?

The Law of Cosines is a vital theorem in trigonometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. In the context of triangle ABC, where a, b, and c are the lengths of the sides opposite to angles A, B, and C respectively, the Law of Cosines specifically states that:

b² = a² + c² - 2ac Cos B

This equation defines how the cosine of angle B can be derived from the lengths of the sides of the triangle. Here is how it works:

1. The term a² + c² represents the sum of the squares of the lengths of sides a and c.

2. The term -2ac Cos B accounts for the relationship between angle B and the sides a and c. This negative term is essential because it adjusts the sum of the squares of the other two sides based on how angle B influences the triangle's shape.

By rearranging this equation, one can derive the expression for Cos B if needed. It succinctly captures the geometric relationships inherent in the triangle due to the angle B.

The expression provided in the correct answer captures the relationship accurately, demonstrating how the lengths