MCQ
If $A + B = 225^\circ ,$ then $\frac{{\cot A}}{{1 + \cot A}}.\frac{{\cot B}}{{1 + \cot B}} = $
- A$1$
- B$-1$
- C$0$
- ✓$1/2$
$= \frac{1}{{(1 + \tan A)\,(1 + \tan B)}}$ $ = \frac{1}{{\tan A + \tan B + 1 + \tan A\tan B}}$ $[\,\because \tan (A + B) = \tan {225^o}]$
$ \Rightarrow \,\tan \,A + \tan \,B = 1 - \tan \,A\,\tan B$
$ = \frac{1}{{1 - \tan A\,\tan B + 1 + \tan A\tan B}} $
$= \frac{1}{2}$.
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