Correct Answer: 2

Solution : (1+ sin ⁴ A – cos ⁴ A) cosec ² A
= [1+ (sin ² A) ² – (cos ² A) ² ] cosec ² A
= [1+ (sin ² A + cos ² A)(sin ² A – cos ² A)] cosec ² A
= [1+ sin ² A – cos ² A] cosec ² A
= [ sin ² A + (1–  cos ² A)] cosec ² A
= [ sin ² A +  sin ² A ] cosec ² A
= 2sin ² A × cosec ² A
= 2
Hence, the correct answer is 2.