Q3. If $$tan 2A \ = \ cot (A – 18°)$$, where 2A is an acute angle, find the value of A.

Given,

$$tan 2A = cot (A – 18°)$$

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

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

=> $$2A + A \ = \ 18° + 90°$$

=> $$3A \ = \ 108°$$

=> $$A \ = \ 36°$$