Learn 6 new identities:
cos(x + y) = cos(x) * cos(y) - sin(x) * sin(y)
cos(x - y) = cos(x) * cos(y) + sin(x) * sin(y)
sin(x + y) = sin(x) * cos(y) + cos(x) * sin(y)
sin(x - y) = sin(x) * cos(y) - cos(x) * sin(y)
tan(x + y) = tan(x) + tan(y) / 1 - (tan(x))(tan(y))
tan(x - y) = tan(x) - tan(y) / 1 + (tan(x))(tan(y))