solve the equation on the interval 0, 2π).\n√2 cos x - 1 = 0\nx = π/?, π/

Explanation:

Step1: Isolate cosine function

Add 1 to both sides of $\sqrt{2}\cos x - 1=0$ and then divide by $\sqrt{2}$. $\cos x=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}$

Step2: Find solutions in given interval

We know that $\cos x=\frac{\sqrt{2}}{2}$ has solutions $x = \frac{\pi}{4}$ and $x=\frac{7\pi}{4}$ in the interval $[0, 2\pi)$.

Answer:

$x=\frac{\pi}{4},\frac{7\pi}{4}$