# Are there any solutions for this equation within (0,2π)? [cosx=sinx] if so, what are they?

$x = \frac{\pi}{4} , \frac{5 \pi}{4}$
Examining the unit circle, we see where $\cos x = \sin x$, or where $\left(x , y\right) = \left(x , x\right)$:
$x = \frac{\pi}{4} , \frac{5 \pi}{4}$