If A + B = 225^ , then A 1 + A . B 1 + B = - Vidyadip

MCQ

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

A
$1$
B
$-1$
C
$0$
✓
$1/2$

✓

Answer

Correct option: D.

$1/2$

d
(d) $\frac{{\cot A}}{{1 + \cot A}}\,.\,\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}}$ $[\,\because \tan (A + B) = \tan {225^o}]$

$ \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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