Trigonometric identities are equations that describe relationships between the various trigonometric functions. The trigonometric functions are a set of functions that are employed in the study of angles and angular relationships in planar and 3-dimensional figures. Development of the trigonometric identities was simultaneous with the development of the functions themselves. Claudius Ptolemy, one of the most influential Greek astronomers, was developing the identities in terms of chords of a circle or arcs as early as about 130. He showed that he knew one of the most important identities, sin (x + y) = sin x cos y + cos x sin y although instead of writing it in terms of sin and cos he used chords as they did in those times, very early in his career while studying astronomy.

The trigonometric identities are derived by expressing the sine or cosine of a sum of difference of angles in terms...