WAEC - Further Mathematics (2008 - No. 21)
Express \(\frac{1}{1 - \sin 45°}\) in surd form.
\(2 + \sqrt{2}\)
\(2 + \sqrt{3}\)
\(2 - \sqrt{2}\)
\(1 + 2\sqrt{2}\)
Explicació
\(\sin 45 = \frac{\sqrt{2}}{2}\)
\(\frac{1}{1 - \sin 45} = \frac{1}{1 - \frac{\sqrt{2}}{2}}\)
\(\frac{2}{2 - \sqrt{2}} = \frac{4 + 2\sqrt{2}}{4 - 2}\)
= \(2 + \sqrt{2}\)