1. 14. DOUBLE-ANGLE IDENTITIES

2. If we want to know a formula for we could use the sum formula.
we can trade these places

3. Let's try the same thing for
This is the double angle formula for cosine but by substiuting some identities we can express it in a couple other ways.

4. Double-angle Formula for Tangent

5. Summary of Double-Angle Formulas

6. Double-Angle Identities
Simplify

7. Double-Angle Identities
Simplify

8. Double-Angle Identities
Simplify

9. Double-Angle Identities
Simplify

10. Double-Angle Identities
Verify the identity

11. Double-Angle Identities
Verify the identity

12. Identities
Prove

13. Let's draw a picture. 5 4   -3

14. Let's draw a picture.  1  4