Question : If $\sin 2\theta=\frac{\sqrt{3}}{2}$, then what is the value of $\tan \theta$?
Option 1: $\frac{1}{2}$
Option 2: $1$
Option 3: $\frac{1}{ \sqrt{3}}$
Option 4: $\sqrt{3}$
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Correct Answer: $\frac{1}{ \sqrt{3}}$
Solution :
$\sin 2\theta = \frac{\sqrt{3}}{2}$
⇒ $\sin 2\theta = \sin 60° $
⇒ $2\theta = 60° $
⇒ $\theta = 30° $
So, $\tan \theta = \tan 30° = \frac{1}{\sqrt{3}}$
Hence, the correct answer is $\frac{1}{\sqrt{3}}$.
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