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CSMC 2018 Part A Problem 6

Source:

November 24, 2018
CSMCCSMC 2018

Problem Statement

Suppose that 0∘<A<90∘0^\circ < A < 90^\circ and 0∘<B<90∘0^\circ < B < 90^\circ and (4+tan⁡2A)(5+tan⁡2B)=320tan⁡Atan⁡B\left(4+\tan^2 A\right)\left(5+\tan^2 B\right) = \sqrt{320}\tan A\tan B Determine all possible values of cos⁡Asin⁡B\cos A\sin B.
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