Question

If 2 sin 2θ = $\sqrt{3}$, then θ = ?
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer 1

(a) 30^o

$$\begin{gathered} 2\sin 2\theta =\sqrt{3} \\ \Rightarrow \sin 2\theta =\frac{\sqrt{3}}{2}=\sin {60}^{\mathrm{o}} \\ \Rightarrow \sin 2\theta =\sin {60}^{\mathrm{o}} \\ \Rightarrow 2\theta ={60}^{\mathrm{o}} \\ \Rightarrow \theta ={30}^{\mathrm{o}} \end{gathered}$$