Question

If $\tan A-\tan B=xand\cot B-\cot a=y$ , then the value of $\cot (A-B)$ is

• A. x-y
• B. x+y
• C. $\frac{1}{x}-\frac{1}{y}$
• D. $\frac{1}{x}+\frac{1}{y}$

Answer 1

The correct option is D $\frac{1}{x}+\frac{1}{y}$

$\cot B-\cot A=y$
$\tan A-\tan B$
or $\frac{\tan A-\tan B}{\tan A\tan B}=y$
or $\tan A\tan B=\frac{x}{y}$
Now, $cot(A-B)=\frac{1}{\tan (A-B)}=\frac{1+\tan A\tan B}{\tan A-\tan B}$
$=\frac{1+\frac{x}{y}}{x}=\frac{1}{x}+\frac{1}{y}$