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Answer :
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]
\( 4A + A \ = \ 20° + 90° \)
=> \( 5A \ = \ 110° \)
=> \( A \ = \ 22° \)