Question

If $tan\theta =\frac{1}{2}$ and $tan\varphi =\frac{1}{3}$, then the value of $\theta +\varphi$ is

• A. $\frac{\pi }{6}$
• B. $\pi$
• C. $0$
• D. $\frac{\pi }{4}$

Answer 1

Answer: (D)

Given, $tan\theta =\frac{1}{2}$ and $tan\varphi =\frac{1}{3}$

$\therefore tan\left(\theta +\varphi \right)=\frac{tan\theta +tan\varphi }{1-tan\theta tan\varphi }$

$=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2}\times \frac{1}{3}}=\frac{\frac{5}{6}}{\frac{5}{6}}=1$

$\Rightarrow \theta +\varphi =\frac{\pi }{4}$