Question 56

$$\left(\frac{2\tan30^{\circ}}{1-\tan^230^{\circ}}\right)$$ =

Solution

$$\left(\frac{2\tan30^{\circ}}{1-\tan^230^{\circ}}\right)=\frac{2\left(\frac{1}{\sqrt{3}}\right)}{1-\left(\frac{1}{\sqrt{3}}\right)^2}$$

$$=\frac{2\left(\frac{1}{\sqrt{3}}\right)}{1-\frac{1}{3}}$$

$$=\frac{\frac{2}{\sqrt{3}}}{\frac{2}{3}}$$

$$=\frac{3}{\sqrt{3}}$$

$$=\sqrt{3}$$

Hence, the correct answer is Option A

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