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[tex]y^2 \leq p^pq^q.(\frac{cos^2x}{p})...(\frac{sin^2q}{q}) \leq p^pq^q.(\frac{\frac{p.cos^2x}{p}+\frac{q.sin^2x}{q}}{q+p})^{p+q} \leq p^pq^q(\frac{cos^2x+sin^2x}{q+p})^{q+p} \rightarrow y \leq \sqrt{(\frac{p}{q+p})^p.\frac{q}{q+p})^q}[/tex]DHBK Hà nội 1996
Đẳng thức [tex]\rightarrow \frac{cos^2x}{p}=\frac{sin^2x}{q} \rightarrow tanx=\sqrt{\frac{q}{p}} (0 \leq x \leq \frac{\pi}{2})[/tex]
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