Question

If ${\tan }^{-1}x-{\tan }^{-1}y={\tan }^{-1}A$, then $A$ is equal to

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

Answer 1

Answer: (C)

Given that, ${\tan }^{-1}x-{\tan }^{-1}y={\tan }^{-1}A$
$\Rightarrow {\tan }^{-1}\left(\frac{x-y}{1+xy}\right)={\tan }^{-1}A$
$\therefore A=\frac{x-y}{1+xy}$