They both have an equals sign, but an Equation and an Identity are two very different beasts.

An Equation is a statement that is true only for *certain values* of the variable. For example, '2x = 10'.

This equation is only true for the specific value x=5. For any other value, it is false.

An Identity is a statement that is true for *all possible values* of the variable. For example, '2(x+1) = 2x + 2'.

No matter what you plug in for x (0, 7, -100), this statement will always be true.

An equation is a puzzle to be solved. An identity is a fundamental truth to be recognized.

You solve an equation. You simplify or prove an identity.

In trigonometry, you will encounter many identities, like sin²(x) + cos²(x) = 1, which are true for any angle x.

Confusing the two can lead to big problems. If you try to 'solve' an identity, you'll end up with a statement like '0=0'.

An equation is a question. An identity is a law of the universe. Knowing the difference is crucial.