^ - 1 a - b 1 + ab + ^ - 1 b - c 1 + bc = - Vidyadip

MCQ

${\tan ^{ - 1}}\frac{{a - b}}{{1 + ab}} + {\tan ^{ - 1}}\frac{{b - c}}{{1 + bc}} = $

A
${\tan ^{ - 1}}a - {\tan ^{ - 1}}b$
✓
${\tan ^{ - 1}}a - {\tan ^{ - 1}}c$
C
${\tan ^{ - 1}}b - {\tan ^{ - 1}}c$
D
${\tan ^{ - 1}}c - {\tan ^{ - 1}}a$

✓

Answer

Correct option: B.

${\tan ^{ - 1}}a - {\tan ^{ - 1}}c$

b
(b) ${\tan ^{ - 1}}\left( {\frac{{a - b}}{{1 + ab}}} \right) + {\tan ^{ - 1}}\left( {\frac{{b - c}}{{1 + bc}}} \right)$

$ = {\tan ^{ - 1}}(a) - {\tan ^{ - 1}}(b) + {\tan ^{ - 1}}(b) - {\tan ^{ - 1}}(c)$

$ = {\tan ^{ - 1}}(a) - {\tan ^{ - 1}}(c)$.

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