Question Number 18834 by mondodotto@gmail.com last updated on 30/Jul/17
Answered by Tinkutara last updated on 30/Jul/17
$$\mathrm{tan}\:\mathrm{2A}\:=\:\mathrm{cot}\:\left(\mathrm{90}°\:−\:\mathrm{2A}\right)\:=\:\mathrm{cot}\:\left(\mathrm{A}\:−\:\mathrm{18}°\right) \\ $$$$\mathrm{Since}\:\mathrm{A}\:\mathrm{is}\:\mathrm{acute},\:\mathrm{so}\:\mathrm{cot}\:\mathrm{A}\:=\:\mathrm{cot}\:\mathrm{B}\:\Leftrightarrow\:\mathrm{A}\:=\:\mathrm{B} \\ $$$$\mathrm{90}°\:−\:\mathrm{2A}\:=\:\mathrm{A}\:−\:\mathrm{18}° \\ $$$$\mathrm{A}\:=\:\mathrm{36}° \\ $$