The halfangle identities are trigonometric identities that express the sine and cosine of a halfangle in terms of the sine and cosine of a single angle.
The identities can be derived in several ways^{[1]}. One of the ways to derive the identities is shown below using the geometry of an inscribed angle on the unit circle:
The halfangle identities express the cosine and sine of a halfangle in terms of the sine and cosine of the single angle.

Derive Half Angle Identities (Algebra) Example