RU-ALLRUSSIAN 1984 Problem 5

Let $\mathrm{A} = \cos^2 \mathrm{a}$ , $\mathrm{B} = \sin^2 \mathrm{a}$ . Show that for all real a and positive x, y we have $\mathrm{x}^\mathrm{A}\mathrm{y}^\mathrm{B} < \mathrm{x} + \mathrm{y}$ .