[73] - Algebraic Inequalities from and for Math Contests

Να αποδείξετε ότι, για κάθε $0<x\le \pi/2$, \[\frac{\sin x}{x}+\frac{(\sin x)^4}{x^4}\ge 2\cos x+(\cos x)^2(\sin x)^4.\] Proposed by Paolo Perfetti, Università di "Tor Vergata'', Italy