Question

Solve for $x\in [0^{\circ },{90}^{\circ }]$:

${\cos }^2{30}^{\circ }+{\cos }^2{x}^{\circ }=1$

Answer 1

${\cos }^{2}30+{\cos }^{2}x=1$
${\left(\frac{\sqrt{3}}{2}\right)}^2+{\cos }^{2}x=1$
${\cos }^{2}x=\frac{1}{4}$
$\cos x=\frac{1}{2}$
$\cos x=\cos 60$
$x={60}^{\circ }$