If A - B = x and B - A = y, then (A - B) = - Vidyadip

MCQ

If $\tan A - \tan B = x$ and $\cot B - \cot A = y,$ then $\cot (A - B) = $

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

✓

Answer

Correct option: D.

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

d
(d) $\cot \,(A - B) = \frac{1}{{\tan \,(A - B)}} $

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

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

$= \frac{1}{x} + \frac{1}{y}$.

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