1. Sum and Difference Identities
Objective
To use the sum and difference identities for the sine, cosine, and tangent functions

2. Sum and Difference Identities for the Sin Function
Sum and Difference Identities for the Cos Function
cos (a + b) = cos a cos b – sin a sin b
cos (a – b) = cos a cos b + sin a sin b
Sum and Difference Identities for the Sin Function
sin (a + b) = sin a cos b + cos a sin b
sin (a – b) = sin a cos b – cos a sin b
Sum and Difference Identities for the Tan function
tan a + tan b
1 - tan a tan b
tan (a + b) =
tan a – tan b
1 + tan a tan b
tan (a – b) =

3. Find cos 15° cos 15° = cos (45° - 30°)
= cos 45° cos 30° + sin 45° sin 30° √2 2 √3 2 √2 2 1 2 = ∙ + ∙ √6 4 √2 4 = +
√6 + √2 4 =

4. Find sin 15°
sin 15° = sin (45° - 30°)
= sin 45° sin 30° - cos 45° sin 30° √2 2 √3 2 √2 2 1 2 = ∙ - ∙ √6 4 √2 4 - =
√6 - √2 4 =

5. Find tan 105°
tan 105° = tan ( 60° + 45°)
tan 60° + tan 45°
1 – tan 60° tan 45° = √
1 - √3 ∙ 1 =
√3 + 1
1 - √3
1 + √3 = ∙
= √3

6. If sin a = 5/13 and cos b = 4/5, find cos (a + b)
cos ( a + b) = cos a cos b – sin a sin b

7. Assignment
6.4 Exercises