Double Angle Identities

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]


  1. Derive Double Angle Identities (Algebra) Example
  2. Derive Double Angles Identities (Unit Circle) Example
  3. Derive Double Angles Identities (Complex Plane) Example