Correct option is (C) \(\frac 1{\sqrt 3}\)
Given,
\(\tan (\alpha+\beta) =\sqrt{3}\)
\(\tan (\alpha+\beta) =\tan 60^{\circ}\)
\(\alpha+\beta =60^{\circ} \quad....(i)\)
\(\tan \alpha =\frac{1}{\sqrt{3}} \)
\(\tan \alpha =\tan 30^{\circ} \)
\(\alpha =30^{\circ}\quad ....(ii)\)
Putting the value of eq (ii) in eq (i),
\(\alpha+\beta =60^{\circ}\)
\(30^{\circ}+\beta =60^{\circ}\)
\(\beta =60^{\circ}-30^{\circ} \)
\(\therefore \beta=30^{\circ}\)
\( \tan \beta=\tan 30^\circ\)
\(\therefore \tan \beta=\frac{1}{\sqrt{3}}\)
