Question 53

The value of $$(\cosec A + \cot A + 1)(\cosec A - \cot A + 1) - 2 \cosec A$$ is:

Solution

$$(cosecA+cotA+1)(cosecA-cotA+1)-2cosecA$$

= $$(cosecA + 1)^2 - (cotA)^2 - 2cosecA$$

($$\because a^2 - b^2 = (a + b)(a - b)$$)

= $$cosec^2A + 1 + 2cosecA - cot^2A - 2cosecA$$

($$cosec^2A - cot^2A = 1)

= 1 + 1 = 2

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