Identity (mathematics)

In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables within a certain range of validity.^[1] In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined. For example, ${\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}}$ and ${\displaystyle \cos ^{2}\theta +\sin ^{2}\theta =1}$ are identities.^[1] Identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign.^[2] Formally, an identity is a universally quantified equality.