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Q.

If $(1 - \cot A) (1 - \cot B) = 2$ then

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a

$A + B = \frac{π}{2}$

b

$A - B = \frac{π}{4}$

c

$A + B = \frac{π}{4}$

d

$A = B$

answer is A.

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Detailed Solution

$\begin{array}{l} (1 - \cot A) (1 - \cot B) = 2 \\ \Rightarrow 1 - \cot A - \cot B + \cot A \cot B = 2 \\ \Rightarrow \cot A \cot B - 1 = \cot A + \cot B \\ \Rightarrow \frac{\cot A \cot B - 1}{\cot A + \cot B} = 1 \\ \Rightarrow \cot (A + B) = \cot 45 ° \\ \Rightarrow A + B = \frac{π}{4} \end{array}$

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