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Question Number 158534 by HongKing last updated on 05/Nov/21

$$\mathrm{Prove}\mathrm{that}{\mathrm{a}}^2{\tan }^{\mathbf{k}}\mathrm{x}+{\mathrm{b}}^2{\sin }^{\mathbf{k}}\mathrm{x}>{2\mathrm{abx}}^{\mathbf{k}}$$ $$\mathrm{for}\mathrm{all}\mathrm{x}\in (0;\frac{\pi }{2})\mathrm{and}\mathrm{positive}\mathrm{integer}\mathbf{k}$$ $$$$

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