Question

If $\sqrt{3}\tan 2\mathrm{\theta }-3=0\mathrm{then}\mathrm{\theta }=?$
(a) 15°
(b) 30°
(c) 45°
(d) 60°

Answer 1

As we know that,
​$$\begin{gathered} \tan 60°=\sqrt{3} \\ \mathrm{Thus}, \\ \mathrm{if}\sqrt{3}\tan 2\theta -3=0 \\ \Rightarrow \sqrt{3}\tan 2\theta =3 \\ \Rightarrow \tan 2\theta =\frac{3}{\sqrt{3}} \\ \Rightarrow \tan 2\theta =\sqrt{3} \\ \Rightarrow 2\theta =60° \\ \Rightarrow \theta =30° \\ \mathrm{Hence},\mathrm{the}\mathrm{correct}\mathrm{option}\mathrm{is}\left(\mathrm{b}\right). \end{gathered}$$