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

The correct option is D $\frac{\pi }{4}$

$\therefore \tan (\theta +\varphi )=\frac{\tan \theta +\tan \varphi }{1-\tan \theta .\tan \varphi }$$=\frac{(\frac{1}{2}+\frac{1}{3})}{(1-\frac{1}{2}.\frac{1}{3})}=1$
$\Rightarrow \theta +\varphi =\frac{\pi }{4}$