$(1 + c o t 81^{0}) (1 + c o t 54^{0})$ equals to:

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-2

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Solution

The correct option is A 2
$cot (135^{0}) = cot (180^{0} - 45^{0}) = - cot 45^{0} = (- 1)$
$cot (135^{0}) = - 1 = cot (81 + 54) = \frac{{cot 81}^{0} {cot 54}^{0} - 1}{{cot 81}^{0} + cot 54^{0}} = (- 1)$
So, ${cot 81}^{0} {cos 54}^{0} - 1 = - {cot 81}^{0} - {cot 54}^{0}$
${cot 81}^{0} {cot 54}^{0} + {cot 81}^{0} + {cot 54}^{0} + 1 = 2$
${cot 81}^{0} ({cot 54}^{0} + 1) + ({cot 54}^{0} + 1) = 2$
So, $(1 + {cot 81}^{0}) \times (1 + {cot 54}^{0}) = 2$

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