What does the cosine of the sum of angles look like, cos(a + b)?

The cosine of the sum of angles formula expresses how to calculate the cosine of the sum of two angles, ( a ) and ( b ). The correct representation is given by the formula:

[

\cos(a + b) = \cos(a)\cos(b) - \sin(a)\sin(b)

]

This formula indicates that when finding the cosine of the sum of two angles, one multiplies the cosine of each angle together and subtracts the product of their sines. This relationship comes from the properties of the unit circle and the geometric interpretations of these trigonometric functions.

The formula reflects the way the angles combine in terms of their respective sines and cosines, maintaining consistency in the behavior of these functions in relation to one another. It’s essential for solving problems involving angle addition in a variety of mathematical contexts, including calculus, physics, and engineering. Understanding this relationship helps form a solid foundation for more complex trigonometric identities and applications.