Correct Answer: Option A

Explanation

\(\sin 45 = \frac{\sqrt{2}}{2}\)

\(\frac{1}{1 - \sin 45} = \frac{1}{1 - \frac{\sqrt{2}}{2}}\)

\(\frac{2}{2 - \sqrt{2}} = \frac{4 + 2\sqrt{2}}{4 - 2}\)

= \(2 + \sqrt{2}\)

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