1. Copyright © Cengage Learning. All rights reserved.
5.4
SUM AND DIFFERENCE FORMULAS
Copyright © Cengage Learning. All rights reserved.

2. What You Should Learn
Use sum and difference formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations.

3. Using Sum and Difference Formulas
In this section, we will study the uses of several trigonometric identities and formulas.
Example 1 shows how sum and difference formulas can be used to find exact values of trigonometric functions involving sums or differences of special angles.

4. Example 1 – Evaluating a Trigonometric Function
Find the exact value of

5. Example 2
Find the exact value of cos 75.

6. Example 3
Find the exact value of cos(u + v) given sin u = 7/25 where 0 < u < /2, and cos v = -4/5 where /2 < v < .

7. Example 4
Write sin(arctan 1 + arccos x) as an algebraic expression.

8. Example 5 – Proving a Cofunction identity
Prove the cofunction identity
= sin x.

9. Using Sum and Difference Formulas
Sum and difference formulas can be used to rewrite expressions such as
and , where n is an integer as expressions involving only sin  or cos  .
The resulting formulas are called reduction formulas.

10. Example 6
Simplify each expression. a. b.

11. Example 7 – Solving a Trigonometric Equation
in the interval
Find all solutions of