If cot A . cot B = 2, then what is the value of cos(A + B) . sec(A - B) ?

1/3

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-1

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Solution

The correct option is B 1/3
Given $cot A cot B = 2$
$\Rightarrow \frac{cos A}{sin A} . \frac{cos B}{sin B} = 2 \Rightarrow cos A c o s B = 2 sin A sin B \Rightarrow cos (A - B) = cos A cos B + sin A sin B = 3 sin A sin B \Rightarrow cos (A + B) = cos A cos B - sin A sin B = sin A sin B$
Now $cos (A + B) . sec (A - B) = \frac{cos (A + B)}{cos (A - B)} = \frac{sin A sin B}{3 sin A sin B} = \frac{1}{3}$

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