Question Number 211115 by Durganand last updated on 28/Aug/24
Answered by som(math1967) last updated on 28/Aug/24
$${tanA}+\mathrm{2}{tan}\mathrm{2}{A}+\frac{\mathrm{4}}{{tan}\mathrm{2}.\mathrm{2}{A}} \\ $$$$={tanA}+\mathrm{2}{tan}\mathrm{2}{A}+\frac{\mathrm{4}\left(\mathrm{1}−{tan}^{\mathrm{2}} \mathrm{2}{A}\right)}{\mathrm{2}{tan}\mathrm{2}{A}} \\ $$$$={tanA}+\frac{\mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{A}+\mathrm{2}−\mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{A}}{{tan}\mathrm{2}{A}}\: \\ $$$$={tanA}\:+\frac{\mathrm{2}}{{tan}\mathrm{2}{A}}\: \\ $$$$={tanA}+\frac{\left(\mathrm{1}−{tan}^{\mathrm{2}} {A}\right)}{{tanA}} \\ $$$$=\frac{{tan}^{\mathrm{2}} {A}+\mathrm{1}−{tan}^{\mathrm{2}} {A}}{{tanA}} \\ $$$$=\frac{\mathrm{1}}{{tanA}}={cotA} \\ $$$$ \\ $$