Which trigonometric identity can be used to simplify the integral of 2sin(x)cos(x)?

The identity that can be used to simplify the integral of 2sin(x)cos(x) is indeed sin(2x) = 2sin(x)cos(x). This identity highlights that the expression 2sin(x)cos(x) is equivalent to sin(2x).

When dealing with integrals, this simplification is valuable because it allows us to convert the integral of a product of sine and cosine functions into a simpler form using a single trigonometric function, which is typically easier to integrate.

For instance, when you have the integral ∫2sin(x)cos(x) dx, applying the identity results in ∫sin(2x) dx, which can be directly integrated to give you -½ cos(2x) + C, where C is the constant of integration.

The other options, such as the cosine double angle identity and the Pythagorean identity or the tangent definition, do not directly aid in simplifying the integral of 2sin(x)cos(x) in the same straightforward manner. Therefore, recognizing and applying the correct trigonometric identity is crucial for efficient integration in this case.