Question
If $2\sin\theta=\sqrt{3},$ prove that $\theta=30^\circ.$
✓
Answer
$2\sin(2\theta)=\sqrt3$$\Rightarrow\sin(2\theta)=\frac{\sqrt3}{2}$
$\Rightarrow\sin(2\theta)=\sin(60)^\circ$
$\Rightarrow2\theta=60^\circ$
$\Rightarrow\theta=\frac{60^\circ}{2}$
$\Rightarrow\theta=30^\circ$
$\Rightarrow\sin(2\theta)=\sin(60)^\circ$
$\Rightarrow2\theta=60^\circ$
$\Rightarrow\theta=\frac{60^\circ}{2}$
$\Rightarrow\theta=30^\circ$
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