For example is $\sin^2x+\cos^2x=1$ an "identity" or "formula"?
If they're different, please give an example of an identity that isn't a formula and an example of a formula that isn't an identity.
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Have you tried searching the Wikipedia pages for these terms? – Toby Mak Mar 18 '20 at 07:39
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The term formula has a wider scope than identity. Roughly speaking, the term identity is used when you are implicitly adding universal quantifiers in the front. Thus $$ a^2 - b^2 = (a+b)(a-b) $$ is an identity since it holds for all $a$ and $b$. The term formula can be used to define a function or a sequence. For instance, you could say "let $u_n$ be the sequence defined by the formulas $u_0 = 2$ and $u_{n+1}= 1 +u_n^2$".
That being said, both terms also have a precise definition in logic. I let you read this wikipedia article for more detials.
J.-E. Pin
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A formula always has 2 or more variables and is used to find an unknown quantity while value of variables from an identity cannot be find out as they infinite solutions.ex of formula can be like W=mg where we have one value and use that to find the other while a plus b whole squared equals a squared plus b squared plus 2ab is an identity if u have value of a you can't find value of b.
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2Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Mar 18 '20 at 07:02