1. 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) =

2. 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 =

3. 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 =

4. 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

5. 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