Algebra and Trigonometry, 5th Edition

7.3 Proving Trigonometric Identities

• Prove identities using other identities.

• Use the product-to-sum identities and the sum-to-product identities to derive other identities.

The Logic of Proving Identities

We outline two algebraic methods for proving identities.

Hints for Proving Identities

1. Use either method 1 or method 2.

2. Work with the more complex side first.

3. Carry out any algebraic manipulations, such as adding, subtracting, multiplying, or factoring.

4. When rational expressions are involved, it can be helpful to multiply by forms of 1 to obtain a common denominator.

5. Converting all expressions to sines and cosines is often helpful.

6. Try something! Put your pencil to work and get involved. You will be amazed at how often this leads ...