What is the sum formula for sin(a + b)?

The sum formula for sin(a + b) is indeed given by the expression sin(a)cos(b) + cos(a)sin(b). This formula reflects how to break down the sine of a sum into its components based on the angles involved.

To understand why this is the correct expression, consider how sine and cosine functions interact with each other through the properties of a unit circle or their respective geometric definitions. When you add two angles, the result can be viewed as a combination of the effects of both angles on the sine function—this is captured in the formula.

In this formula, sin(a) and cos(b) represent the contributions from the angle 'a', while cos(a) and sin(b) represent the contributions from the angle 'b'. It neatly combines the two contributions in a way that geometrically makes sense when visualizing the rotation induced by both angles on the unit circle.

The other options do not correspond with the established identity for the sine of a sum, either providing forms for other trigonometric functions or incorrect combinations of the sine and cosine functions. Thus, the choice capturing both sine and cosine contributions accurately reflects the relationship at play when adding two angles together in the sine function.