Given that sin 60 o = \(\frac{\sqrt{3}}{2}\) and cos 60 o = \(\frac{1}{2}\), evaluate \(\frac{1
MATHEMATICS
WAEC 2009
Given that sin 60o = \(\frac{\sqrt{3}}{2}\) and cos 60o = \(\frac{1}{2}\), evaluate \(\frac{1 - sin 60^o}{1 + cos 60^o}\)
- A. \(\frac{2 + \sqrt{3}}{3}\)
- B. \(\frac{1 - \sqrt{3}}{3}\)
- C. \(\frac{1 + \sqrt{3}}{3}\)
- D. \(\frac{2 - \sqrt{3}}{3}\)
Correct Answer: D. \(\frac{2 - \sqrt{3}}{3}\)
Explanation
Sin 60 = \(\frac{\sqrt{3}}{2}\); cos 60o = \(\frac{1}{2}\)
= \(\frac{1 - \sin 60}{1 + \cos 60} = \frac{1 - \frac{\sqrt{3}}{2}}{1 + \frac{1}{2}}\)
= \(\frac{2 - \sqrt{3}}{3}{2}\div \frac{2 + 1}{2}\)
= \(\frac{2 - \sqrt{3}}{2} \times \frac{2}{3}\)
= \(\frac{2 - \sqrt{3}}{3}\)
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