According to the Law of Cosines, which formula represents Cos A?

The Law of Cosines is a fundamental theorem in triangle geometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. The formula states that for a triangle with sides (a), (b), and (c) opposite to angles (A), (B), and (C) respectively, the following relationship holds:

[ a^2 = b^2 + c^2 - 2bc \cdot \cos A ]

This equation allows you to find the length of one side of a triangle when you know the lengths of the other two sides and the angle between them, or to find the cosine of an angle when you know the lengths of all three sides.

To isolate (\cos A), we can rearrange the Law of Cosines formula:

1. Start with the Law of Cosines:

[ a^2 = b^2 + c^2 - 2bc \cdot \cos A ]

2. Rearranging gives:

[ 2bc \cdot \cos A = b^2 + c^2 - a^2 ]

3. Dividing both sides by (2bc) results