example of identity a m×a n
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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][2] 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.[2] Identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign.[3]Visual proof of the Pythagorean identity: for any angle {\displaystyle \theta }, The point {\displaystyle (x,y)=(\cos \theta ,\sin \theta )} lies on the unit circle, which satisfies the equation {\displaystyle x^{2}+y^{2}=1} Thus, {\displaystyle \cos ^{2}\theta +\sin ^{2}\theta =1}