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,

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

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

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

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