What does the double angle formula for sin(2x) simplify to?

The double angle formula for sin(2x) is derived from the angle addition formulas in trigonometry. Specifically, it can be expressed as sin(2x) = sin(x + x). Using the angle addition formula, this expands to sin(x)cos(x) + sin(x)cos(x), which simplifies to 2sin(x)cos(x).

This formula reveals that the sine of double angles can be calculated using the sine and cosine of the original angle. Thus, the correct answer, 2sin(x)cos(x), directly represents this relationship.

Choosing this option confirms an understanding of how trigonometric identities apply to double angles and reflects knowledge of the geometric interpretation behind these formulas.