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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