What does the formula sin[x(+/-)y] express?

The formula sin[x(+/-)y] refers to the sine of a sum or difference of two angles, which is expressed mathematically by the sine addition and subtraction identities. Specifically, for any angles x and y, the identities are:

• sin(x + y) = sin(x)cos(y) + cos(x)sin(y)

• sin(x - y) = sin(x)cos(y) - cos(x)sin(y)

These two formulas combine to form the expression sin[x(+/-)y], meaning you would apply the addition or subtraction based on the sign in the brackets.

The correct answer accurately reflects this principle, outlining how the sine function responds to the addition and subtraction of its angles by incorporating cosine functions and maintaining the relationship between the angles. This is fundamental in trigonometry and is essential for solving various mathematical problems involving sine functions.

Other options do not align with these established identities. They either reference incorrect relationships or fail to incorporate the essential components of cosine and sine necessary for the sum/difference identities.