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Class-11-commerce»Maths

if cotAcotB=2

show that cos(A+B)/cos(A-B)=1/3

$\frac{\cos (A + B)}{\cos (A - B)} = \frac{\cos A \cos B - \sin Asin B}{\cos A \cos B + \sin Asin B} = \frac{\cot A \cot B - 1}{\cot A \cot B + 1} [Multiplying and dividing by sin A sin B] = \frac{2 - 1}{2 + 1} [Putting cot A cot B = 2] = \frac{1}{3}$

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