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Express \frac{1}{1 - \sin 45°} in surd form. ...

Express \frac{1}{1 - \sin 45°} in surd form. 

A.

2 + \sqrt{2}

B.

2 + \sqrt{3}

C.

2 - \sqrt{2}

D.

1 + 2\sqrt{2}

Correct answer is A

\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}