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If $\tan A=3 / 4$ and $\tan B=-12 / 5$, then how many values can cot $(A-B)$ have depending on the actual values of $A$ and $B ?$
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The correct answer is:
4
$\tan \mathrm{A}=\frac{3}{4}$ and $\tan \mathrm{B}=-\frac{12}{5}$
$\therefore \quad \cot (\mathrm{A}-\mathrm{B})=\frac{1}{\tan (\mathrm{A}-\mathrm{B})}=\frac{1+\tan \mathrm{A} \tan \mathrm{B}}{\tan \mathrm{A}-\tan \mathrm{B}}$
$\therefore \quad \cot (\mathrm{A}-\mathrm{B})=\frac{1}{\tan (\mathrm{A}-\mathrm{B})}=\frac{1+\tan \mathrm{A} \tan \mathrm{B}}{\tan \mathrm{A}-\tan \mathrm{B}}$
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