Find the exact value of each expression. (Do not use a calculator.)
cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)

Key Concepts

Cosine and Sine Addition Formulas

The cosine and sine addition formulas are fundamental identities in trigonometry that express the cosine and sine of the sum of two angles. Specifically, cos(a + b) = cos(a)cos(b) - sin(a)sin(b) and sin(a + b) = sin(a)cos(b) + cos(a)sin(b). These formulas allow us to simplify expressions involving trigonometric functions of sums of angles, which is essential for solving the given problem.

Reference Angles

Reference angles are the acute angles formed by the terminal side of an angle in standard position and the x-axis. They help in determining the values of trigonometric functions for angles that are not standard. In this problem, understanding the reference angles for 7π/9 and 2π/9 is crucial for evaluating the cosine and sine functions accurately.

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is a key tool in trigonometry for defining the sine and cosine of angles. By using the unit circle, we can find the exact values of trigonometric functions for various angles, including those expressed in radians like 7π/9 and 2π/9, which are necessary for solving the expression in the question.