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) =

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 =

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 =

Find tan 105° tan 105° = tan ( 60° + 45°) tan 60° + tan 45° 1 – tan 60° tan 45° = √3 + 1 1 - √3 ∙ 1 = √3 + 1 1 - √3 1 + √3 = ∙ = -2 - √3

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