Question Number 172480 by Shrinava last updated on 27/Jun/22
$$\mathrm{In}\:\mathrm{acute}\:\bigtriangleup\mathrm{ABC}\:\mathrm{holds}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\prod}\:\left(\mathrm{tan}\:\mathrm{A}\right)^{\boldsymbol{\mathrm{a}}} \:\:\leqslant\:\:\underset{\boldsymbol{\mathrm{cyc}}} {\prod}\:\left(\mathrm{cot}\:\frac{\mathrm{A}}{\mathrm{2}}\right)^{\frac{\boldsymbol{\mathrm{b}}\:+\:\boldsymbol{\mathrm{c}}}{\mathrm{2}}} \\ $$