Question

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Answer 1

Answer:

Given ,

To prove cot^4 A -1 = cosec^4 A - 2 cosec^2 A

R.H.S. = cosec^4 A - 2cosec^2 A

          = cosec^2 A ( cosec^2 A - 2)

          = (1 + cot^2 A)( 1 + cot^2 A - 2)

          = (1 + cot^2 A) ( cot^2 A - 1)

          (We know (a+b)(a-b) = a^2 - b^2)

          = (cot^2 A)^2 - 1^2

          = cot^4 A - 1 = L.H.S.

Hence proved

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