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Question Number 18834 by mondodotto@gmail.com last updated on 30/Jul/17

Answered by Tinkutara last updated on 30/Jul/17

tan 2A = cot (90° − 2A) = cot (A − 18°)  Since A is acute, so cot A = cot B ⇔ A = B  90° − 2A = A − 18°  A = 36°

$$\mathrm{tan}\:\mathrm{2A}\:=\:\mathrm{cot}\:\left(\mathrm{90}°\:−\:\mathrm{2A}\right)\:=\:\mathrm{cot}\:\left(\mathrm{A}\:−\:\mathrm{18}°\right) \\ $$$$\mathrm{Since}\:\mathrm{A}\:\mathrm{is}\:\mathrm{acute},\:\mathrm{so}\:\mathrm{cot}\:\mathrm{A}\:=\:\mathrm{cot}\:\mathrm{B}\:\Leftrightarrow\:\mathrm{A}\:=\:\mathrm{B} \\ $$$$\mathrm{90}°\:−\:\mathrm{2A}\:=\:\mathrm{A}\:−\:\mathrm{18}° \\ $$$$\mathrm{A}\:=\:\mathrm{36}° \\ $$

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