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)

$\tan \theta=\frac{1}{2}, \tan \phi=\frac{1}{3}$
$\tan (\theta+\phi)=\frac{\tan \theta+\tan \phi}{1-\tan \theta \tan \phi}$
$=\frac{\frac{1}{2}+\frac{1}{3}}{1-\left(\frac{1}{2}\right)\left(\frac{1}{3}\right)}$
$=\frac{\frac{5}{6}}{\frac{5}{6}}$
$\therefore \tan (\theta+\phi)=1$
$\Rightarrow \theta+\phi=\frac{\pi}{4}$