If \( sec 4 A \ = \ cosec (A – 20°) \) , where 4 A is an acute angle, find the value of A.

Given, \( sec 4A \ = \ cosec (A – 20°) \)
We know that, \( cosec(90° - \theta ) \ = \ sec\theta \)

=> \( cosec (90°– 4A) \ = \ sec 4A \)

∴ \( cosec (90° – 4A) \ = \ cosec (A – 20°) \)

=> \( 90° – 4A \ = \ A – 20° \) [\(\because \) (90° – 4A) and (A – 20°) are both acute angles]

\( 4A + A \ = \ 20° + 90° \)

=> \( 5A \ = \ 110° \)

=> \( A \ = \ 22° \)