Half Angle Identities

The half angle identities express the cosine and sine of a half-angle in terms of the sine and cosine of the single angle. The identities can be derived using the geometry of the inscribed angle shown below:

Double Angle Identities

The half-angle identities can also be derived using the double angle formulas and the previous theorems derived above.

Derive Half Angle Identities (Algebra) | Example

The half-angle identities can be derived from the double angle identities by transforming the angles using algebra and then solving for the half-angle expression.