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Let S be the set of all real values of x with 0 < x < \frac{\pi}{2} such that \sin x, \cos x, and \tan x form the side lengths (in some order) of a right triangle. Compute the sum of \tan^2 x over all x in S.

 Mar 29, 2021
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The sum of all possible values of tan^2 x is 1 + sqrt(3).

 Mar 30, 2021

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