Prove that (sin^4-cos^4+1)cosec^2A=2
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Answer:
LHS =(sin⁴A- cos⁴A+1)cosec²A
= [(sin²A)²-(cos²A)²+1)cosec²A
= [(sin²A+cos²A)(sin²A-cos²A)+1]cosec²A
= (sin²A-cos²A+1)cosec²A
/* By Trigonometric identity:
sin²A+cos²A = 1 */
= (sin²A+1-cos²A)cosec²A
= (sin²A+sin²A)cosec²A
= 2sin²Acosec²A
= 2sin²A × (1/sin²A)
= 2
= RHS
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