Question

A positive acute angle is divided into two parts whose tangents are $\frac{1}{2}$ and $\frac{1}{3}$ Then, the angle is

• A. $\frac{\pi}{4}$
• B. $\frac{\pi}{5}$
• C. $\frac{\pi}{3}$
• D. $\frac{\pi}{6}$

Answer 1

Answer: (A)

According to the question,

$\theta=tan^{-1}\frac{1}{2}+tan^{-1}\frac{1}{3}$

$=tan^{-1} \left(\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\cdot\frac{1}{3}}\right)$

$=tan^{-1}\left(\frac{5/ 6}{5 /6}\right)=tan^{-1}\left(1\right)$

$=\frac{\pi}{4}$