Question

Solve equation for 0 < x < 2pi

Answer 1

$\sqrt2\cos x-1=0$
$\sqrt2\cos x=1$
$\cos x=\dfrac1{\sqrt2}$

This occurs twice in the interval $0\le x\le2\pi$, when $x=\dfrac\pi4$ and $x=\dfrac{3\pi}4$.