Determine the value of x that satisfies the equation: $\cos x-\sin x=0$

Step 1 ：Given the equation \(\cos x - \sin x = 0\).

Step 2 ：We can rewrite the equation as \(\cos x = \sin x\).

Step 3 ：We know that \(\sin x\) and \(\cos x\) are equal when x is equal to \(\frac{\pi}{4}\) or \(\frac{5\pi}{4}\) in the interval \([0, 2\pi]\).

Step 4 ：Substituting these values into the equation confirms that the function equals zero for the values of x equal to \(\frac{\pi}{4}\) and \(\frac{5\pi}{4}\).

Step 5 ：Therefore, the values of x that satisfy the equation \(\cos x - \sin x = 0\) are \(\boxed{\frac{\pi}{4}}\) and \(\boxed{\frac{5\pi}{4}}\).