What Is the Sin2(x) Identity?

The main identity for sin2(x), where the sine function is squared, is sin2(x) + cos2(x) = 1, which can be rewritten as 1 - cos2(x) = sin2(x). That identity is known as either the Pythagorean or basic identity.

The double-angle identity of sin2(x) is sin2(x) = cos2(x) - cos(2x). That identity can also be expressed as 1 - 2sin2(x) = 2cos2(x) - 1. Using the half-angle identity, sin2(x) can be expressed as ½[1 – cos(2x)]. In math, the identity of a trigonometric function, such as sine, is defined as rule that is always true for the function for any value of x.