The answer to the first question can be derived from the Departure equation.
Departure = Change in longitude x cosine of latitude.
Dividing both sides by cosine of latitude gives
Departure / cosine of latitude = Change of longitude
The secant of an angle = 1/cosine, so dividing by the cosine is the same as multiplying by the secant.
So departure x secant of latitude = Change of longitude.
Deriving answers is this way will enable you to develop a far better understanding of the subjects.