Part 1/6:

Understanding the Cosine Addition and Subtraction Formulas

Trigonometry can sometimes feel daunting, especially when trying to remember various formulas. However, the addition and subtraction formulas for cosine offer straightforward solutions that are essential in many mathematical applications. This article will explore these formulas, provide a geometric intuition behind them, and demonstrate their proofs.

The Cosine Addition Formula

Let’s start with the cosine addition formula:

cos(x + y) = cos x * cos y - sin x * sin y

This formula states that the cosine of the sum of two angles can be computed using the cosines and sines of the individual angles.