IMO Shortlist 1966 problem 5


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Prove the inequality
\tan \frac{\pi \sin x}{4\sin \alpha} + \tan \frac{\pi \cos x}{4\cos \alpha} >1
for any x, \alpha with 0 \leq x \leq \frac{\pi }{2} and \frac{\pi}{6} < \alpha < \frac{\pi}{3}.
Izvor: Međunarodna matematička olimpijada, shortlist 1966