Express \(\frac{1}{1 - \sin 45°}\) in surd form.
FURTHER MATHEMATICS
WAEC 2008
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: A. \(2 + \sqrt{2}\)
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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