General solution of trigonometric equation$\sqrt{1-\cos x}=\sin x$

$\sqrt{1-\cos x}=\sin x$, here $\sin x\ge 0$

$\Rightarrow x\in \left[2n\pi ,\left(2n+1\right)\pi \right]$

$\text{Also\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}1-\cos x={\sin }^{2}x$

$\Rightarrow 1-\cos x=1-{\cos }^{2}x$

$\Rightarrow {\cos }^{2}x-\cos x=0$

$\Rightarrow \cos x=0or\cos x=1$

$\Rightarrow x=n\pi +\frac{\pi }{2}$ or $x=2n\pi$