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[1]. 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