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Question Number 157585 by MathSh last updated on 24/Oct/21

$$\mathrm{if}0<\mathrm{a}⩽\mathrm{b}⩽\mathrm{c}<\frac{\pi }{2}\mathrm{then}:$$$$\frac{5}{\tan \mathbf{a}}+\frac{3}{\tan \mathbf{b}}+\frac{1}{\tan \mathbf{c}}⩾\frac{27}{\tan \mathbf{a}+\tan \mathbf{b}+\tan \mathbf{c}}$$

Answered by ghimisi last updated on 25/Oct/21

$$3(\frac{1}{tga}+\frac{1}{tgb}+\frac{1}{tgc})+2(\frac{1}{tga}-\frac{1}{tgc})⩾$$$$3\cdot \frac{9}{tga+tgb+tgc}+\frac{2(tgc-tga)}{tgatgc}⩾\frac{27}{tga+tgb+tgc}$$

Commented by MathSh last updated on 25/Oct/21

$$\mathrm{Thank}\mathrm{you}\mathrm{so}\mathrm{much}\mathrm{dear}\mathbf{S}\mathrm{er}\mathrm{very}\mathrm{nice}$$

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