Question

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

Answer 1

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

$\tan (\theta +\varphi )=\frac{\tan \theta +\tan \varphi }{1-\tan \theta .\tan \varphi }$

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

$=\frac{5}{5}$

$\tan (\theta +\varphi )=1$

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

$(\theta +\varphi )=\frac{\pi }{4}$