The value of $x$ in $[-2\pi ,2\pi ],$ for which the graph of the function $y=\sqrt{\frac{1+\sin x}{1-\sin x}}-\sec x$ and  $y=-\sqrt{\frac{1-\sin x}{1+\sin x}}+\sec x,$ coincide are:

$$\begin{gathered} y=\sqrt{\frac{1+\sin x}{1-\sin x}}-\frac{1}{\cos x} \\ =\frac{1+\sin x}{\left|\cos x\right|}-\frac{1}{\cos x}=[\begin{array}{c}\frac{\sin x}{\cos x}if\cos x>0\\ -\frac{2+\sin x}{\cos x}if\cos x<0\end{array} \\ again y=-\sqrt{\frac{1-\sin x}{1+\sin x}}+\frac{1}{\cos x} \\ \frac{1}{\cos x}-\frac{1-\sin x}{\left|\cos x\right|}=[\begin{array}{c}\frac{\sin x}{\cos x}if\cos x>0\\ \frac{2-\sin x}{\cos x}if\cos x<0\end{array} \end{gathered}$$

Hence for Identical graph  $\cos x>0.$