Question

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

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

Answer 1

Answer: (D)

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

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

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

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