Question

If $2\sin 2\theta =\sqrt{3}$ then the value of $\theta$ is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

$2sin2\theta =\sqrt{3}$

$\Rightarrow sin2\theta =\frac{\sqrt{3}}{2}$

$\because sin{60}^{\circ }=\frac{\sqrt{3}}{2}$

$\therefore sin2\theta =sin{60}^{\circ }$

$\Rightarrow 2\theta ={60}^{\circ }$

$\Rightarrow \theta =\frac{60}{2}={30}^{\circ }$