Question

If $\frac{1+\tan \theta }{1-\tan \theta }=\sqrt{3}$, then find the value of $\theta$

• A. $30^{\circ }$
• B. $25^{\circ }$
• C. $15^{\circ }$
• D. $45^{\circ }$

Answer 1

Answer: (C)

$\frac{1+\tan \theta }{1-\tan \theta }=\sqrt{3}$
$\frac{\tan 45+\tan \theta }{1-\tan 45-\tan \theta }=\sqrt{3}$
$\tan \left(45^{\circ }+\theta \right)=\tan 60^{\circ }$
$\Rightarrow 45^{\circ }+\theta =60^{\circ }$
$\theta =60^{\circ }-45^{\circ }=15^{\circ }$