An identity is an equality relation A = B, such that A and B contain

some variables and give the same result when the variables are

substituted by any values (usually ). In other words, A = B is an

identity if A and B define the same functions. This means that

an identity is an equality between functions that are differently

defined. For example

(x + y)2 = x2 + 2xy + y2and cos2(x) + sin2(x) = 1 are identities.

Identities were sometimes indicated by the triple bar symbol ≡

instead of the equals sign =, but this is no longer a common usage.