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Question Number 90483 by M±th+et£s last updated on 23/Apr/20

prove that/ ((sin^3 a)/(sin b))+((cos^3 a)/(cos b))≥sec(a−b)  for all a,b∈ (0,(π/2))

$${prove}\:{that}/\:\frac{{sin}^{\mathrm{3}} {a}}{{sin}\:{b}}+\frac{{cos}^{\mathrm{3}} {a}}{{cos}\:{b}}\geqslant{sec}\left({a}−{b}\right) \\ $$$${for}\:{all}\:{a},{b}\in\:\left(\mathrm{0},\frac{\pi}{\mathrm{2}}\right) \\ $$

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