There are dozens of Trigonometric Identities. We will only list the ones we have used. Clarifier: there may be three identities in a family and we only use one but we show the whole family.
Pythagorean Identities
Sum and Difference
cos(x)cos(y) – sin(x)sin(y) = cos(x+y)
cos(x)cos(y) + sin(x)sin(y) = cos(x-y)
sin(x)cos(y) + cos(x)sin(y) = sin(x+y)
sin(x)cos(y) – cos(x)sin(y) = sin(x-y)