Cosec^6A -cot^6A =3cot^2A.cosec^2A+1
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Step-by-step explanation:
cosec^6A-cot^6A
=(cosec²A)³-(cot²A)³
=(cosec²A-cot²A) (cosec⁴A+cosec²Acot²A+cot⁴A)
=cosec⁴A+cot⁴A+cosec²Acot²A
=(cosec²A)²+(cot²A)²+2cosec²Acot²A -2cosec²Acot²A+cosec²Acot²A
=(cosec²A)²+(cot²A)²-2cosec²Acot²A +3cosec²Acot²A
=(cosec²A-cot²A)²+3cosec²Acot²A
=1+3cot²Acosec²A
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