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Question-211115




Question Number 211115 by Durganand last updated on 28/Aug/24
Answered by som(math1967) last updated on 28/Aug/24
tanA+2tan2A+(4/(tan2.2A))  =tanA+2tan2A+((4(1−tan^2 2A))/(2tan2A))  =tanA+((2tan^2 2A+2−2tan^2 2A)/(tan2A))   =tanA +(2/(tan2A))   =tanA+(((1−tan^2 A))/(tanA))  =((tan^2 A+1−tan^2 A)/(tanA))  =(1/(tanA))=cotA
$${tanA}+\mathrm{2}{tan}\mathrm{2}{A}+\frac{\mathrm{4}}{{tan}\mathrm{2}.\mathrm{2}{A}} \\ $$$$={tanA}+\mathrm{2}{tan}\mathrm{2}{A}+\frac{\mathrm{4}\left(\mathrm{1}−{tan}^{\mathrm{2}} \mathrm{2}{A}\right)}{\mathrm{2}{tan}\mathrm{2}{A}} \\ $$$$={tanA}+\frac{\mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{A}+\mathrm{2}−\mathrm{2}{tan}^{\mathrm{2}} \mathrm{2}{A}}{{tan}\mathrm{2}{A}}\: \\ $$$$={tanA}\:+\frac{\mathrm{2}}{{tan}\mathrm{2}{A}}\: \\ $$$$={tanA}+\frac{\left(\mathrm{1}−{tan}^{\mathrm{2}} {A}\right)}{{tanA}} \\ $$$$=\frac{{tan}^{\mathrm{2}} {A}+\mathrm{1}−{tan}^{\mathrm{2}} {A}}{{tanA}} \\ $$$$=\frac{\mathrm{1}}{{tanA}}={cotA} \\ $$$$ \\ $$

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