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.
 Using the double angle identities and algebra^{[1]}
 Using the inscribed angle theorem and the unit circle^{[2]}
 Using the trigonometry of complex numbers^{[3]}
The halfangle identities express the cosine and sine of a halfangle 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:

Derive Half Angle Identities (Algebra)Wumbo (internal)

Derive Half Angle Identities (Inscribed Angle)Wumbo (internal)

Derive Half Angle Identities (Complex Plane)Wumbo (internal)