If A+B=225^{circ},then the value of frac{cot | vedclass

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(D) Let $X = \frac{\cot A}{1+\cot A} \cdot \frac{\cot B}{1+\cot B}$.Converting to $	an$ functions: $X = \frac{1/	an A}{1+1/	an A} \cdot \frac{1/	a

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$\frac{1}{2}$

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(D) Let $X = \frac{\cot A}{1+\cot A} \cdot \frac{\cot B}{1+\cot B}$.Converting to $	an$ functions: $X = \frac{1/	an A}{1+1/	an A} \cdot \frac{1/	an B}{1+1/	an B} = \frac{1}{	an A+1} \cdot \frac{1}{	an B+1}$.$X = \frac{1}{	an A 	an B + 	an A + 	an B + 1}$.Given $A+B = 225^{\circ}$,we have $	an(A+B) = 	an(225^{\circ}) = 1$.Using the formula $	an(A+B) = \frac{	an A + 	an B}{1 - 	an A 	an B} = 1$,we get $	an A + 	an B = 1 - 	an A 	an B$.Substituting this into the denominator: $	an A 	an B + (1 - 	an A 	an B) + 1 = 2$.Thus,$X = \frac{1}{2}$.

If $A+B=225^{\circ}$,then the value of $\frac{\cot A}{1+\cot A} \cdot \frac{\cot B}{1+\cot B}$ is equal to

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