Which formula correctly represents the cosine of a sum or difference?

The formula for the cosine of a sum or difference is derived from trigonometric identities and is fundamental in trigonometry. The correct expression for the cosine of the sum of two angles, ( x ) and ( y ), is given by:

[

\cos(x \pm y) = \cos(x)\cos(y) \mp \sin(x)\sin(y)

]

This shows that when adding angles ( x ) and ( y ), the cosine of the sum will have a negative sign in front of the sine term, while the cosine of the difference will have a positive sign in front of the sine term. Both forms can be captured in the expression provided in the correct answer.

In the context of the available choices, the formula represented in the correct answer accurately captures the necessary structure of these identities, clearly distinguishing between the sum and difference, which is crucial for the proper application in trigonometric calculations.