If angle x is in the fourth quadrant and angle y is in the first quadrant, the value of cos (x-y) is

-y) = cos x cos y + sin x sin y becomes, in terms of sign,

cos (x-y) = (Note that cos (x-y) = cos x cos y + sin x sin y.

If angle x is in the fourth quadrant, then sin x is positive and cos x is negative.

If angle y is in the first quadrant, then sin y is positive and cos y is positive.

Then cos (x-y) becomes, in terms of sign:

(-) (+) + (+) (+), or

(-) + (+)

This would be positive, overall, if cos x cos y < sin x sin y.