The double angle identities are trigonometric identities that give the cosine and sine of a double angle in terms of the cosine and sine of a single angle.
Two additional double angle identities are sometimes given that combine the pythagorean identity and the cosine identity above using algebra.
The double identities can be derived a number of ways:
 Using the sum of two angles identities and algebra^{[1]}
 Using the inscribed angle theorem and the unit circle^{[2]}
 Using the the trigonometry of the complex plane^{[3]}

Derive Double Angle Identities (Algebra) Example

Derive Double Angles Identities (Unit Circle) Example

Derive Double Angles Identities (Complex Plane) Example