1 + cos^2 A/1+cosecA = cosecA
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1 +cot^2A/(1+cosec A) = cosec A
I presume the brackets as i have shown are correct as the question is incomplete without them.
LHS = 1 +cot^2A/(1+cosec A)
= 1 + ( cosec^2 -1)/[1+ cosec A]
= 1+ (cosec x+1)(cosec x -1)/[1+ cosec A]
= 1 + cosec x -1
= cosec x = RHS
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