Maths and the formulae for double and compound angles
sin(A + B)
sinAcosB + cosAsinB
sin(A - B)
sinAcosB - cosAsinB
cos(A + B)
cosAcosB - sinAsinB
cos(A - B)
cosAcosB + sinAsinB
tan(A + B)
tanA + tanB/1 - tanAtanB
tan(A - B)
tanA - tanB/1 + tanAtanB
sin2A
2sinAcosA
cos2A
2cos²A - 1 = 2cos²A - 2sin²A = 2 - 2sin²A
tan2A
2tanA/1 - tan²A