If ^ - 1 x - ^ - 1 y = ^ - 1 A, then A - Vidyadip

MCQ

If ${\tan ^{ - 1}}x - {\tan ^{ - 1}}y = {\tan ^{ - 1}}A,$ then $A$

A
$x - y$
B
$x + y$
✓
$\frac{{x - y}}{{1 + xy}}$
D
$\frac{{x + y}}{{1 - xy}}$

✓

Answer

Correct option: C.

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

c
(c) Given that ${\tan ^{ - 1}}x - {\tan ^{ - 1}}y = {\tan ^{ - 1}}A$

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

Hence $A = \frac{{x - y}}{{1 + xy}}$.

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