Solve the trigonometric equation analytically for values of $\displaystyle x$ for $\displaystyle 0\le x <2\pi$

$\displaystyle sin\left(x - \frac{\pi}{4}\right) = cos\left(x - \frac{\pi}{4}\right)$

$\displaystyle sin\;x\;cos\;\frac{\pi}{4} - cos\;x\;sin\;\frac{\pi}{4} = cos\;x\;cos\;\frac{\pi}{4} + sin\;x\;sin\;\frac{\pi}{4}$

$\displaystyle sin\;x\;\left(\frac{\sqrt{2}}{2}\right) - cos\;x\;\left(\frac{\sqrt{2}}{2}\right) = cos\;x\;\left(\frac{\sqrt{2}}{2}\right) + sin\;x\;\left(\frac{\sqrt{2}}{2}\right)$

$\displaystyle 2\;cos\;x\;\left(\frac{\sqrt{2}}{2}\right)$

If what I did so far is right. I'm stuck at this point.