What is an identity in math?

In mathematics, an identity is an equality that holds true for all values of the variables. An identity is often represented as an equation, and it is symbolic rather than numeric. It is a fundamental concept in algebra, calculus, and other branches of mathematics.

For example, x + y = y + x is an identity in algebra. No matter what values of x and y you substitute into the equation, it will always hold true.

Similarly, sin²θ + cos²θ = 1 is an identity in trigonometry. It states that the sum of the squares of sine and cosine functions is always equal to one, for any angle θ.

Identities are valuable in solving mathematical problems, as they often simplify and transform equations to make them easier to work with.