Question

If tan A - tan B = x and, cot B - cot A =y, find cot(A-B).

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

Answer 1

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

$\tan A-\tan B=x$ and, $\cot B-\cot A=y$

Now, $\cot B-\cot A=y$

$\frac{1}{\tan B}-\frac{1}{\tan A}=y$

$\frac{\tan A-\tan B}{\tan A\tan B}=y$

$\tan A\tan B=\frac{x}{y}$

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

$=\frac{1+\tan A\tan B}{\tan A-\tan B}=\frac{x+y}{xy}=\frac{1}{x}+\frac{1}{y}$