cosec^6A-cot^6A=1+3cosec^2Acot^2A
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Step-by-step explanation:
cosec⁶A - cot⁶A = 1+ 3 cosec²A . cot²A
Taking LHS,
cosec⁶A - cot⁶A
= (cosec²A)³ - (cot²A)³
= (cosec²A - cot²A)³+3 cosec²A . cot²A (cosec²A-cot²A)
[ a³-b³= (a-b)³+3ab(a-b) ]
= (1)³+3 cosec²A . cot²A. (1)
= 1 + 3 cosec²A . cot²A = RHS
[ As 1 + cot²x = cosec²x ]
[ Then cosec²x - cot²x = 1 ]
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