If A + C = B, then A , B , C = - Vidyadip

MCQ

If $A + C = B,$ then $\tan A\,\tan B\,\tan C = $

A
$\tan A\,\tan B + \tan \,C$
✓
$\tan \,B - \tan \,C - \tan \,A$
C
$\tan A + \tan C - \tan B$
D
$ - \,(\tan A\tan B + \tan C)$

✓

Answer

Correct option: B.

$\tan \,B - \tan \,C - \tan \,A$

b
(b) $B = A + C \Rightarrow \tan B = \tan (A + C)$

==> $\tan B = \frac{{\tan A + \tan C}}{{1 - \tan A\tan C}}$

==> $\tan A\tan B\tan C = \tan B - \tan A - \tan C$.

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