Trigonometry! #32

Geometry Level 4

If AA and BB are two angles satisfying 0<A,B<π20<A,B<\frac {\pi}{2} and A+B=π3A+B=\frac {\pi}{3}, then find the minimum value of secA+secB\sec A + \sec B.

If your answer is simplified to ab\frac {a}{b}, where aa and bb have no terms in common (other than one, maybe), enter the value of a2+b2a^{2} + b^{2}.

This problem is part of the set Trigonometry.

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