Evaluate: 2Tan30°/1-tan^2 30°=?

\(\frac{2 tan 30^{\circ}}{1 + tan^{2} 30^{\circ}}\)

As we know, \(tan 30^{\circ} = \frac{1}{\sqrt{3}}\)

Therefore,

=\( \frac{2 tan 30^{\circ}}{1 + tan^{2} 30^{\circ}} = \frac{2 * (\frac{1}{\sqrt{3}})}{ 1 + (\frac{1}{\sqrt{3}})^{2}}\)

=\( \frac{\frac{2}{\sqrt{3}}}{1+\frac{1}{3}}\)

=\( \frac{\frac{2}{\sqrt{3}}}{\frac{4}{3}}\)

=\(\frac{2}{\sqrt{3}} * \frac{3}{4}\)

=\( \frac{2}{\sqrt{3}} * \frac{\sqrt{3} *+ \sqrt{3}}{4}\)

=\( \frac{\sqrt{3}}{2}\)

Therefore, \(\frac{2 tan 30^{\circ}}{1 + tan^{2} 30^{\circ}} = \frac{\sqrt{3}}{2}\)

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