The value of the expression $\sqrt{\frac{1-\sin x}{1+\sin x}}+\sqrt{\frac{1+\sin x}{1-\sin x}}$  is

$\sqrt{\frac{\left(1-\sin x\right)}{\left(1+\sin x\right)}}\times \sqrt{\frac{\left(1-\sin x\right)}{\left(1-\sin x\right)}}+\sqrt{\frac{\left(1+\sin x\right)\left(1+\sin x\right)}{\left(1-\sin x\right)\left(1+\sin x\right)}}$

$=\left|\frac{1-\sin x}{\cos x}\right|+\left|\frac{1+\sin x}{\cos x}\right|$

If $0<x<\frac{\pi }{2}$

$\Rightarrow \frac{1-\sin x+1+\sin x}{\cos x}=\frac{2}{\cos x}$

If  $\frac{\pi }{2}<x<\pi$  and $\frac{3\pi }{2}<x<2\pi$  $$

$\Rightarrow -1+\sin x-1-\sin x=-2$

$\Rightarrow \frac{-2}{\cos x}$