If \( |\tan A|1 \) and \( |A| \) is acute, then \( \frac{\sqrt{(1+\sin 2 A)}+\sqrt{(1-\sin 2 A)}...

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If \( |\tan A|1 \) and \( |A| \) is acute, then \( \frac{\sqrt{(1+\sin 2 A)}+\sqrt{(1-\sin 2 A)}}{\sqrt{(1+\sin 2 A)}-\sqrt{(1-\sin 2 A)}} \) is equal to
(a) \( \tan A \)
(b) \( -\tan A \)
(c) \( \cot A \)
(d) \( -\cot A \)
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