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WAEC Mathematics 2017 Paper

Question : 21

Total: 49

^{\circ}

^{\circ}

\;\frac{3}{2}

^{\circ}

^{\circ}

\;\frac{1}{2}

\;\frac{\tan\;60^{\circ}\;-\;1}{1\;-\;\tan\;30^{\circ}}

Solution:

From the figure above, tan30º = $\;\frac{1}{\sqrt[3]{}}$ and tan60º = $\sqrt{3}$

so $\;\frac{\tan 60 - 1}{1 - \tan 30}$

= $\;\frac{\sqrt{3}}{1} \div (1 - ( \;\frac{1}{\sqrt{3}}$ ))

= $\;\frac{\sqrt{3}\;-\;1}{1} \div \;\frac{\sqrt{3}\;-\;1}{\sqrt[3]{}}$

= $\;\frac{\sqrt{3}\;-\;1}{1} \times \;\frac{\sqrt[3]{}}{\sqrt{3} - 1}$ = $\sqrt{3}$

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