Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value.3x xcos -------- + cos --------2 2

Sum and difference formulas in trigonometry allow us to express the sine and cosine of the sum or difference of two angles in terms of the sines and cosines of those angles. For example, the cosine of the sum of two angles can be expressed as cos(A + B) = cos(A)cos(B) - sin(A)sin(B). Understanding these formulas is essential for simplifying expressions involving trigonometric functions.

Product-to-sum formulas convert products of sine and cosine functions into sums or differences. For instance, the product sin(A)cos(B) can be expressed as (1/2)[sin(A + B) + sin(A - B)]. These formulas are particularly useful for simplifying complex trigonometric expressions and are often employed in integration and solving equations.

Exact values of trigonometric functions refer to the specific values of sine, cosine, and tangent for commonly used angles, such as 0°, 30°, 45°, 60°, and 90°. Knowing these values allows for quick calculations and simplifications in trigonometric problems. For example, cos(60°) = 1/2 and sin(30°) = 1/2 are fundamental to solving many trigonometric equations.