Question

If $\tan (A+B)=\sqrt{3}$ and $\tan A=1,$ then $\tan (A-B)$ is

• A. $\frac{1}{\sqrt{3}}$
• B. $\sqrt{2}$
• C. $0$
• D. $1$

Answer 1

The correct option is A $\frac{1}{\sqrt{3}}$

$\tan (A+B)=\sqrt{3}$

$\Rightarrow A+B={60}^o$

$\tan A=1$

$\Rightarrow A={45}^o$

$\Rightarrow B={60}^o-{45}^o={15}^o$

$\therefore \tan (A-B)=\tan ({45}^o-{15}^o)$

$=\tan {30}^o=\frac{1}{\sqrt{3}}$.