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# If $$tan 2A \ = \ cot (A – 18°)$$, where 2A is an acute angle, find the value of A.

Given,

$$tan 2A = cot (A – 18°)$$

=>$$\ cot(90°–2A) = cot (90° – 18)$$ [ $$\because tan \theta \ = \ cot (90° – \theta )$$ ]

=> $$90° - 2A \ = \ A – 18°$$ [ $$\because (90° – 2A) and (A – 18°) are both acute angle ] => \( 2A + A \ = \ 18° + 90°$$

=> $$3A \ = \ 108°$$

=> $$A \ = \ 36°$$