These formulas are especially helpful when an angle whose function values you
haven't memorized can be expressed as the sum or difference of two angles whose
function values you have memorized.
The following formulas express the values of trigonometric functions of the sum
of angles in terms of sums of the products of functions of single angles.
sin(α + β) = sin(α)cos(β) + cos(α)sin(β) 

cos(α + β) = cos(α)cos(β)  sin(α)sin(β) 

tan(α + β) = 

The following formulas express the values of trigonometric functions of the
difference of angles in terms of sums of the products of functions of single
angles.
sin(α  β) = sin(α)cos(β)  cos(α)sin(β) 

cos(α  β) = cos(α)cos(β) + sin(α)sin(β) 

tan(α  β) = 
