If ^ - 1 x + ^ - 1 y = 4 then - Vidyadip

MCQ

If ${\tan ^{ - 1}}x + {\tan ^{ - 1}}y = \frac{\pi }{4}$ then

A
$x + y - xy = 1$
✓
$x + y + xy = 1$
C
$x + y + xy + 1 = 0$
D
$x + y - xy + 1 = 0$

✓

Answer

Correct option: B.

$x + y + xy = 1$

b
${\tan ^{ - 1}}x + {\tan ^{ - 1}}y = \frac{\pi }{4}$;

${\tan ^{ - 1}}\left( {\frac{{x + y}}{{1 - xy}}} \right) = {\tan ^{ - 1}}1$

$\frac{{x + y}}{{1 - xy}} = 1$;

$x + y + xy = 1$.

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