$(\sec{x}+\tan{x}-1)(\sec{x}-\tan{x}+1)$
$=\,\,$ $(\sec{x}+\tan{x}-1)$ $\times$ $(\sec{x}-\tan{x}+1)$
$=\,\,$ $\big(\sec{x}+(\tan{x}-1)\big)$ $\times$ $\big(\sec{x}-(\tan{x}-1)\big)$
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