The cosine double angle formula is a trigonometric identity that expresses the cosine of twice an angle in terms of the cosine and sine of the original angle. It is useful in simplifying expressions and solving trigonometric equations, and can be expressed in three forms: cos(2θ) = cos²(θ) - sin²(θ), cos(2θ) = 2cos²(θ) - 1, and cos(2θ) = 1 - 2sin²(θ).