Question 34

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Jambmaths question: 

Find the value of $\frac{\tan {{60}^{o}}-\tan {{30}^{o}}}{\tan {{60}^{o}}+\tan {{30}^{o}}}$

Option A: 

$\tfrac{2}{\sqrt{3}}$

Option B: 

$\tfrac{4}{\sqrt{3}}$

Option C: 

$\tfrac{1}{2}$

Option D: 

1

Jamb Maths Solution: 

$\begin{align}  & \tan {{60}^{o}}=\sqrt{3},\text{  }\tan 30=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3} \\ & \frac{\tan {{60}^{o}}-\tan {{30}^{o}}}{\tan {{60}^{o}}+\tan {{30}^{o}}}=\frac{\sqrt{3}-\tfrac{\sqrt{3}}{3}}{\sqrt{3}+\tfrac{\sqrt{3}}{3}}=\frac{\tfrac{3\sqrt{3}-\sqrt{3}}{3}}{\tfrac{3\sqrt{3}+\sqrt{3}}{3}} \\ & =\frac{\tfrac{2\sqrt{3}}{3}}{\tfrac{4\sqrt{3}}{3}}=\frac{2\sqrt{3}}{3}\times \frac{3}{4\sqrt{3}}=\frac{1}{2} \\\end{align}$

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