\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that \(\tan x \ge x\) for every \(x \in [0, \pi/2[\). Hint: study the convexity of \(\tan\) on \([0, \pi/2[\), then apply the tangent-line inequality at \(a = 0\).
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