### Video Summary:

Double-Number Identities
E.g. cos 2A = cos(A + A)
= cos A cos A – sin A sin A
= cos² A – sin² A
Other forms for cos 2A are obtained by substituting either cos² A = 1 – sin² A or sin² A = 1 – cos² A to get
cos 2A = 1 – 2 sin² A or cos 2A = 2 cos² A – 1. Half-angle identities for sine and cosine are used in calculus when eliminating the xy-term from an equation of the form Ax² + Bxy + Cy² + Dx + Ey + F = 0, so the type of conic it represents can be determined.
From the alternative forms of the identity for cos 2A, we can derive three additional identities, e.g.