Question

On interval [0,2pi) cos x=sin x

Answer 1

$\cos x=\sin x$

When $\cos x\neq0$, you can divide through by it on both sides to get

$\dfrac{\cos x}{\cos x}=\dfrac{\sin x}{\cos x}\iff 1=\tan x$

and this occurs for $x=\dfrac\pi4,\dfrac{5\pi}4$.