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 ]

=> \( 2A + A \ = \ 18° + 90° \)

=> \( 3A \ = \ 108° \)

=> \( A \ = \ 36° \)