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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