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tan(sec-1(5/2))

Start with sec-1(5/2), which is the same as cos-1(2/5). So there is a right triangle, where the side adjacent the angle is 2, and the hypotenuse is 5. Solve for the opposite side: sqrt(5² - 2²) = sqrt(21).

Tangent is opposite over adjacent, so the answer is sqrt(21)/2

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