Using the sine angle difference formula, what is sin(A - B)?

The sine angle difference formula expresses the sine of the difference between two angles, A and B, in terms of the sine and cosine of those angles. Specifically, the formula is:

[

\sin(A - B) = \sin A \cos B - \cos A \sin B

]

This formula arises from the more general properties of sine and cosine functions as well as their geometric interpretations involving right triangles and the unit circle.

In the correct option, we see that it correctly follows this formula structure. The term (\sin A \cos B) corresponds to the first part of the equation, which captures the interaction of the sine of the first angle with the cosine of the second angle. The second part, (- \cos A \sin B), accounts for the negative sign in the formula, which reflects the subtraction in the angle difference and establishes how the cosine of the first angle modifies the sine of the second angle.

This correct answer is essential in trigonometry, especially when simplifying expressions or solving equations that involve angles. Understanding this formula allows students to approach problems related to angle differences with greater confidence and accuracy.