Solve 2tan30^circ/1-tan^230^circ

$$\frac { 2 \tan 30 ^ { \circ } } { 1 - \tan ^ { 2 } 30 ^ { \circ } }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Get the value of \tan(30) from trigonometric values table.

$$\frac{2\times \frac{\sqrt{3}}{3}}{1-\left(\tan(30)\right)^{2}}$$

Express 2\times \frac{\sqrt{3}}{3} as a single fraction.

$$\frac{\frac{2\sqrt{3}}{3}}{1-\left(\tan(30)\right)^{2}}$$

Get the value of \tan(30) from trigonometric values table.

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

To raise \frac{\sqrt{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

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

The square of \sqrt{3} is 3.

$$\frac{\frac{2\sqrt{3}}{3}}{1-\frac{3}{3^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{2\sqrt{3}}{3}}{1-\frac{3}{9}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{2\sqrt{3}}{3}}{1-\frac{1}{3}}$$

Subtract \frac{1}{3} from 1 to get \frac{2}{3}.

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

Divide \frac{2\sqrt{3}}{3} by \frac{2}{3} by multiplying \frac{2\sqrt{3}}{3} by the reciprocal of \frac{2}{3}.

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

Cancel out 2\times 3 in both numerator and denominator.

$$\sqrt{3}$$