Question

If $\cot A=2$ and $\cot B=3$, then what is the value of $A+B$?

• A. $\frac{\pi }{6}$
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is D $\frac{\pi }{4}$

$\cot A=2\cot B=3\Rightarrow A={\tan }^{-1}\frac{1}{2}\Rightarrow B={\tan }^{-1}\frac{1}{3}\Rightarrow A+B={\tan }^{-1}\frac{1}{2}+{\tan }^{-1}\frac{1}{3}=\tan \left(\frac{\frac{1}{2}-\frac{1}{3}}{1-\frac{1}{2}\frac{1}{3}}\right)={\tan }^{-1}\left(\frac{\frac{5}{6}}{\frac{5}{6}}\right)={\tan }^{-1}1A+B=\frac{\pi }{4}$