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prove that whole root cosecA-1/cosecA+1 + whole root cosescA + 1/cosec A -1 = 2 sec A

$Given \sqrt{\frac{\csc A - 1}{\csc A + 1}} + \sqrt{\frac{\csc A + 1}{\csc A - 1}} = \frac{\sqrt{\csc A - 1}}{\sqrt{\csc A + 1}} + \frac{\sqrt{\csc A + 1}}{\sqrt{\csc A - 1}} = \frac{\csc A - 1 + \csc A + 1}{\sqrt{\csc^{2} - 1}} = \frac{2 \csc A}{\sqrt{\cot^{2} A}} = \frac{2 \csc A}{\cot A} = \frac{\frac{2}{\sin A}}{\frac{\cos A}{\sin A}} = \frac{2}{\cos A} = 2 \sec A$

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