The half-angle identities are trigonometric identities that express the sine and cosine of a half-angle in terms of the sine and cosine of a single angle.
The identities can be derived in several ways. One of the ways to derive the identities is shown below using the geometry of an inscribed angle on the unit circle:
The half-angle identities express the cosine and sine of a half-angle in terms of the sine and cosine of the single angle.
Derive Half Angle Identities (Algebra) Example