Q6 Matemática  (Tuymaada 2003)

Prove que para cada ${\alpha }_1,{\alpha }_2,\dots ,{\alpha }_n$ no intervalo $(0,\pi /2)$ $$\left(\frac{1}{\mathrm{sen}{\alpha }_1}+\frac{1}{\mathrm{sen}{\alpha }_2}+\dots +\frac{1}{\mathrm{sen}{\alpha }_n}\right)\left(\frac{1}{\cos {\alpha }_1}+\frac{1}{\cos {\alpha }_2}+\dots +\frac{1}{\cos {\alpha }_n}\right)\le$$ $$\le 2{\left(\frac{1}{sin2{\alpha }_1}+\frac{1}{\mathrm{sen}2{\alpha }_2}+\dots +\frac{1}{\mathrm{sen}2{\alpha }_n}\right)}^2.$$ Proposto por A. Khrabrov