Question

If $4{\cos }^{2}x=3$ and $x$ is an acute angle, find the value of $m$ ; where $\sin 2x$ = $\frac{\sqrt{3}}{m}$

Answer 1

$4{\cos }^{2}x=3$
${\cos }^{2}x=\frac{3}{4}$
$\cos x=\frac{\sqrt{3}}{2}$
$\cos x=\cos 30$
$x={30}^{\circ }$
$\sin 2x=\sin 60=\frac{\sqrt{3}}{2}$