Question

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

Answer 1

(b) 30^o

$$\begin{gathered} \sqrt{3}\tan 2\theta -3=0 \\ \Rightarrow \sqrt{3}\tan 2\theta =3 \\ \Rightarrow \tan 2\theta =\frac{3}{\sqrt{3}} \\ \Rightarrow \tan 2\theta =\sqrt{3}[\because \tan {60}^{\mathrm{o}}=\sqrt{3}] \\ \Rightarrow \tan 2\theta =\tan {60}^{\mathrm{o}} \\ \Rightarrow 2\theta ={60}^{\mathrm{o}} \\ \Rightarrow \theta ={30}^{\mathrm{o}} \end{gathered}$$