IfA+B=225^ ,thencotA 1+cotA 1+cotB = - Vidyadip

MCQ

If$A+B=225^{\circ}$,then$\frac{cotA}{1+cotA}\cdot\frac{cotB}{1+cotB}=$

A
1
B
-1
C
$0$
✓
$\frac{1}{2}$

✓

Answer

Correct option: D.

$\frac{1}{2}$

(D)
$\frac{\cot A }{1+\cot A } \cdot \frac{\cot B }{1+\cot B }$
$=\frac{1}{(1+\tan A)(1+\tan B)}$
$=\frac{1}{\tan A+\tan B+1+\tan A \tan B}$
$=\frac{1}{1-\tan A \tan B+1+\tan A \tan B}$
$\cdots\left[\begin{array}{l}\because \tan (A+B)=\tan 225^{\circ} \\ \Rightarrow \tan A+\tan B=1-\tan A \tan B\end{array}\right]$
$=\frac{1}{2}$

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