What is an identity equation?

An identity equation is an equation that is true for all values of the variable or variables involved. In other words, the equation holds true regardless of the values of the variables. Identity equations are often used in mathematics to prove or demonstrate properties or relationships between different mathematical expressions.

For example, one common identity equation is the distributive property, which states that for any real numbers a, b, and c:

a(b + c) = ab + ac

This equation is true for all values of a, b, and c. Another example of an identity equation is the Pythagorean identity in trigonometry, which states:

sin^2(x) + cos^2(x) = 1

This equation is true for all values of the angle x.

Identity equations are important in mathematics because they allow us to simplify complex expressions and equations, and can also be used to prove more advanced mathematical concepts and theorems.