The value of $$(\cosec A + \cot A + 1)(\cosec A - \cot A + 1) - 2 \cosec A$$ is:
$$(cosecA+cotA+1)(cosecA-cotA+1)-2cosecA$$Â
= $$(cosecA + 1)^2 - (cotA)^2 - 2cosecA$$
($$\because a^2 - b^2 = (a + b)(a - b)$$)Â
= $$cosec^2A + 1 +Â 2cosecAÂ - cot^2AÂ - 2cosecA$$
($$cosec^2AÂ - cot^2A = 1)
= 1 + 1 = 2
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