Question : The value of (1+ sin4 A – cos4 A) cosec2 A is:
Option 1: –2
Option 2: 2
Option 3: 1
Option 4: –1
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.
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