Question Number 194697 by cortano12 last updated on 13/Jul/23
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Answered by MM42 last updated on 13/Jul/23
$$\frac{{tanx}−{tan}\mathrm{3}{x}}{{tanx}}=\mathrm{3}\Rightarrow\frac{{tan}\mathrm{3}{x}}{{tanx}}=−\mathrm{2} \\ $$$$\frac{{cotx}}{{cotx}+{cot}\mathrm{3}{x}}=\frac{{tan}\mathrm{3}{x}}{{tanx}+{tan}\mathrm{3}{x}} \\ $$$$=\frac{−\mathrm{2}}{\mathrm{1}−\mathrm{2}}=\mathrm{2}\:\checkmark \\ $$
Answered by Frix last updated on 13/Jul/23
$$\frac{{a}}{{a}−{b}}=\frac{\mathrm{1}}{\mathrm{3}}\:\Rightarrow\:{b}=−\mathrm{2}{a} \\ $$$$\frac{\frac{\mathrm{1}}{{a}}}{\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}}=\mathrm{2} \\ $$