Problem 112 - Algebra and Trigonometry

Question

What is an identity? Give an example.

Step-by-Step Solution

Answer

An identity is an equation that holds true for all possible values of its variables. An example is the trigonometric identity \(sin^2(x) + cos^2(x) = 1\).

Step 1: Define 'Identity'

In mathematics, an identity is an equation that is true no matter what values are chosen for its variables. This means the identity will hold true for all values of the variable.

Step 2: Example of an Identity

A common example of an identity is the trigonometric identity \(sin^2(x) + cos^2(x) = 1\). No matter what value of x is chosen, the left-hand side will always equal the right-hand side. It is hence an identity since it holds true for all possible values of x.