Angle Addition Formulas

Angle addition formulas express trigonometric functions of sums of angles a + b in terms of functions of a and b. 

sin(a + b) = sin a cos b + sin b cos a

sin(a - b) = sin a cos b - sin b cos a

cos(a + b) = cos a cos b - sin a sin b

cos(a - b) = cos a cos b + sin a sin b

tan(a + b) = (tan a + tan b) / (1 - tan a tan b)

tan(a - b) = (tan a - tan b) / (1 + tan a tan b)

sin a + sin b = 2 sin[(a + b) / 2] cos[(a - b) / 2]

sin a - sin b = 2 sin[(a - b) / 2] cos[(a + b) / 2]

cos a + cos b = 2 cos[(a + b) / 2] cos[(a - b) / 2]

cos a - cos b = -2 sin[(a - b) / 2] sin[(a + b) / 2]