If $\mathrm{A}+\mathrm{B}=225^{\circ}$, then $\frac{\cot \mathrm{A}}{1+\cot \mathrm{A}} \cdot \frac{\cot \mathrm{B}}{1+\cot \mathrm{B}}$, if it exists, is equal to

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Aicharya · Accepted Answer

$\begin{aligned} & \frac{\cot A}{1+\cot A} \cdot \frac{\cot B}{1+\cot B} \ & =\frac{1}{(1+	an A)(1+	an B)} \ & =\frac{1}{	an A+	an B+1+	an A 	an B}\end{aligned}$ $\begin{aligned} & =\frac{1}{1-	an A 	an B+1+	an A 	an B} \ & \quad \cdots\left[\begin{array}{l}\because 	an (A+B)=	an 225^{\circ} \ \Rightarrow 	an A+	an B=1-	an A 	an B\end{array}ight] \ & =\frac{1}{2}\end{aligned}$

If $\mathrm{A}+\mathrm{B}=225^{\circ}$, then $\frac{\cot \mathrm{A}}{1+\cot \mathrm{A}} \cdot \frac{\cot…

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