If A = 2 B + B, then 2 (A - B) = - Vidyadip

MCQ

If $\tan A = 2\tan B + \cot B,$ then $2\tan (A - B) = $

A
$\tan B$
B
$2\tan B$
✓
$\cot B$
D
$2\cot B$

✓

Answer

Correct option: C.

$\cot B$

c
(c) $2\,\,\tan \,(A - B) = 2\,\left( {\frac{{\tan A - \tan B}}{{1 + \tan A\tan B}}} \right)$

$ = 2\frac{{(2\tan B + \cot B - \tan B)}}{{1 + (2\,\tan B + \cot B)\,\tan B}} $

$= 2\,\frac{{\tan B + \cot B}}{{2\,(1 + {{\tan }^2}B)}}$

$ = \frac{{\cot B\,({{\tan }^2}B + 1)}}{{(1 + {{\tan }^2}B)}} $

$= \cot B$.

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