If frac{(cot A cot B - 1)}{(cot B + cot A)} = | vedclass

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Question

(C) Given expression: $\frac{\cot A \cdot \cot B - 1}{\cot B + \cot A}$Substitute $\cot 	heta = \frac{1}{	an 	heta}$:$= \frac{\frac{1}{	an A} \cdo

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$\cot (A + B)$

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(C) Given expression: $\frac{\cot A \cdot \cot B - 1}{\cot B + \cot A}$Substitute $\cot 	heta = \frac{1}{	an 	heta}$:$= \frac{\frac{1}{	an A} \cdot \frac{1}{	an B} - 1}{\frac{1}{	an B} + \frac{1}{	an A}}$Simplify the numerator and denominator:$= \frac{\frac{1 - 	an A \cdot 	an B}{	an A \cdot 	an B}}{\frac{	an A + 	an B}{	an A \cdot 	an B}}$$= \frac{1 - 	an A \cdot 	an B}{	an A + 	an B}$Recall the formula $	an (A + B) = \frac{	an A + 	an B}{1 - 	an A \cdot 	an B}$.Therefore,the expression is equal to $\frac{1}{	an (A + B)}$.$= \cot (A + B)$

If $\frac{(\cot A \cot B - 1)}{(\cot B + \cot A)} = x,$ then the value of $x$ is

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