Question Number 176128 by Shrinava last updated on 13/Sep/22
$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:,\:\mathrm{cot}\:\frac{\mathrm{A}}{\mathrm{2}}\:,\:\mathrm{cot}\:\frac{\mathrm{B}}{\mathrm{2}}\:,\:\mathrm{cot}\:\frac{\mathrm{C}}{\mathrm{2}}\:\in\:\mathrm{Q} \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\left(\underset{\boldsymbol{\mathrm{cyc}}} {\prod}\:\mathrm{sin}\:\frac{\mathrm{A}}{\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}} +\:\left(\underset{\boldsymbol{\mathrm{cyc}}} {\prod}\:\mathrm{cos}\:\frac{\mathrm{A}}{\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}} \in\:\mathrm{Q}\:,\:\forall\mathrm{n}\in\mathbb{N} \\ $$
Commented by Rasheed.Sindhi last updated on 13/Sep/22
$$\mathrm{Shrinava}\:\mathrm{sir},\:{are}\:{you}\:{an}\:{old}\:{member} \\ $$$${of}\:{the}\:{forum}?\:{I}\:{mean}\:{have}\:{you}\:{a} \\ $$$${different}\:{ID}\:{in}\:{the}\:{past}? \\ $$