Sum and difference identities are used to find the sine and cosine of the sum or difference of two angles:

  • \boldsymbol{\sin(x + y) = \sin(x)\cos(y) + \cos(x)\sin(y)}
  • \boldsymbol{\cos(x + y) = \cos(x)\cos(y) - \sin(x)\sin(y)}
  • \boldsymbol{\sin(x - y) = \sin(x)\cos(y) - \cos(x)\sin(y)}
  • \boldsymbol{\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)}