Discussion

What is the value of \(\frac{2\tan 30°}{1 - \tan^2 30°}\)?

Answer: A

This is the double-angle formula for the tangent.

\[ \tan 2A = \frac{2\tan A}{1 - \tan^{2}A} \]

With \( A = 30^{\circ} \):

\[ \frac{2\tan 30^{\circ}}{1 - \tan^{2}30^{\circ}} = \tan 60^{\circ} \]

Checking numerically: \( \tfrac{2/\sqrt{3}}{1 - 1/3} = \tfrac{2/\sqrt{3}}{2/3} = \sqrt{3} = \tan 60^{\circ} \).

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