Question : If $\sin 2\theta=\frac{\sqrt{3}}{2}$, then the value of $\sin 3\theta$ is equal to $(0^{\circ}\leq \theta\leq 90^{\circ})$:
Option 1: $\frac{1}{2}$
Option 2: $1$
Option 3: $0$
Option 4: $\frac{\sqrt{3}}{2}$
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Correct Answer: $1$
Solution :
$\sin 2\theta=\frac{\sqrt{3}}{2}=\sin 60^{\circ}$
$⇒2\theta = 60^{\circ}$
$⇒\theta = 30^{\circ}$
We know that,
$\sin 3\theta = \sin 90^{\circ} = 1$
Hence, the correct answer is $1$.
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