600 degrees is the same thing as -120 degrees (600=360*2-120), now

sec(600) = 1/cos(-120) = 1/cos(120) = -1/cos(60) =-2/sqrt(3)

(you are expected to know that cos(60)=sqrt(3)/2)

315 degrees is the same thing as -45 degrees (315=360-45), now

cot(315) = cot(-45) = 1/tan(-45) = -1/tan(45) = -1

(you are expected to know that tan(45) = 1).

so:

sec(600) + cot(315) = 2/sqrt(3) - 1.

RonL