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Answer:
LHS
= 1/cot^2(cosec -1/1+cos ) - 1/sin^2 (cos -1 / 1+ cosec )
= 1/cosec^2 -1 (cosec -1 / 1+ cos ) +1/1-cos^2 (1-cos/1+cosec)
= 1/(cosec+1)(1+cos) + 1/(1+cos)(1+cosec)
= 2/(1+cos)(1+1/sin) = 2sin/(1+cos)(1+sin)