The Taylor series expansion of cos(x) is a powerful tool used to approximate the value of the cosine function at a given input value. It is derived using the concept of derivatives and involves expressing the cosine function as an infinite sum of terms, each involving a power of x and a coefficient calculated using the derivatives of cos(x). The Taylor series expansion of cos(x) is widely used in various fields, including mathematics, physics, and engineering, for approximating the cosine function accurately for small values of x.