Question

If $4{\cos }^{2}x=3$ and $x$ is an acute angle, find the value of $x$ in degrees.

Answer 1

$4{\cos }^{2}x=3$
${\cos }^{2}x=\frac{3}{4}$
$\cos x=\pm \frac{\sqrt{3}}{2}$
Neglect the negative value, as the angle is acute
$\cos x=\cos 30$
$x={30}^{\circ }$