IMO Shortlist 1966 problem 5
Dodao/la:
arhiva2. travnja 2012. Prove the inequality
![\tan \frac{\pi \sin x}{4\sin \alpha} + \tan \frac{\pi \cos x}{4\cos \alpha} >1](/media/m/d/4/b/d4be47191a2078e4b4430f9f77f8db87.png)
for any
![x, \alpha](/media/m/0/9/b/09bdf79d4b0d3f59a8738575186d9919.png)
with
![0 \leq x \leq \frac{\pi }{2}](/media/m/f/2/2/f22cc10015036b01dd70fca52547ee41.png)
and
%V0
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