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$$(cosecA+cotA+1)(cosecA-cotA+1)-2cosecA$$
= $$(cosecA + 1)^2 - (cotA)^2 - 2cosecA$$
($$\because a^2 - b^2 = (a + b)(a - b)$$)
= $$cosec^2A + 1 + 2cosecA - cot^2A - 2cosecA$$
($$cosec^2A - cot^2A = 1)
= 1 + 1 = 2
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