Please Prove:
(sin^4 theta - cos ^ 4 theta + 1) cosec ^2 theta =2
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R.H.S.
= 2
L.H.S.
= (sin⁴A - cos⁴A + 1) cosec²A
= [(sin²A)² - (cos²A)² + 1] cosec²A
= [(sin²A + cos²A)(sin²A - cos²A) + 1] cosec²A
= {(1)[(sin²A - (1 - sin²A)] + 1} cosec²A
... (sin²A + cos²A = 1 => cos²A = 1 - sin²A)
= (sin²A - 1 + sin²A + 1) cosec²A
= 2sin²Acosec²A = 2(1) ... (sinAcosecA = 1)
= 2
= R.H.S.
•.• L.H.S. = R.H.S.
.•. (sin⁴A - cos⁴A + 1) cosec²A = 2
... Hence Proved!
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