Question

If $2\cos 2A=\sqrt{3}$ and A is acute, find $\sin 3A$.

• A. $\frac{3}{\sqrt{2}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{2}$
• D. $0$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

$2\cos 2A=\sqrt{3}$
$\cos 2A=\frac{\sqrt{3}}{2}(\cos 30°=\frac{\sqrt{3}}{2})$
$\cos 2A=\cos 30°$
$2A=\cos 30°$
$A=15°$
$\sin 3A=\sin 3\left(15°\right)=\sin 45°=\frac{1}{\sqrt{2}}$
So, option B is the correct option.