36.9+ 53.1= 90.0 so if x is in degrees, yes, that is true. If we let y= x+ 36.9, then x- 53.1= y- 36.9- 53.1= y- 90.
But cos(y- 90)= cos(90- y) (since cosine is an even function) and it is always true that sin(y)= cos(90- y).
I have just transformed these equations from 3 cos x - 4 sin x using the alpha method.