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

(A) 1

(B) -1

(C) 0

(D) $1 / 2$

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Best answer

SOLUTION —

$\frac{\cot A}{1+\cot A} \cdot \frac{\cot B}{1+\cot B}$

$ =\frac{1}{(1+\tan A)(1+\tan B)}$

$=\frac{1}{\tan A+\tan B+1+\tan A \tan B}$

$ =\frac{1}{2}$

So, The correct option will be (D).

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