What mathematical identity states that Sin(2x) equals 2SinxCosx?

The mathematical identity that states Sin(2x) equals 2SinxCosx is known as the Double Angle Identity. This identity is fundamental in trigonometry and helps simplify expressions involving sine functions, especially when working with angles that are multiples of a given angle.

The Double Angle Identity essentially allows you to express the sine of a double angle in terms of the sine and cosine of the single angle. This is particularly useful for solving equations, integrating trigonometric functions, and simplifying complex expressions.

For instance, if you want to find Sin(60°), you can use this identity to find Sin(120°) using the angle 60°:

Sin(120°) = Sin(2 * 60°) = 2 * Sin(60°) * Cos(60°).

This relationship not only provides a straightforward calculation path but also reveals the inherent connections between the different trigonometric functions.

The other choices do not define this specific relationship:

• The Law of Sines focuses on the ratios of the lengths of the sides of a triangle to the sine of its opposite angles, which does not pertain to this identity.

• The Pythagorean Identity relates the squares of sine and cosine but does not