Solve 3tan60^circ-2cos30^circ/tan30^circ

$$\frac { 3 \tan 60 ^ { \circ } - 2 \cos 30 ^ { \circ } } { \tan 30 ^ { \circ } }$$

Evaluate

$$6$$

Solution Steps

Get the value of \tan(60) from trigonometric values table.

$$\frac{3\sqrt{3}-2\cos(30)}{\tan(30)}$$

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

$$\frac{3\sqrt{3}-2\times \frac{\sqrt{3}}{2}}{\tan(30)}$$

Cancel out 2 and 2.

$$\frac{3\sqrt{3}-\sqrt{3}}{\tan(30)}$$

Combine 3\sqrt{3} and -\sqrt{3} to get 2\sqrt{3}.

$$\frac{2\sqrt{3}}{\tan(30)}$$

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

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

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

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

Rationalize the denominator of \frac{2\sqrt{3}\times 3}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{6\times 3}{3}$$

Multiply 6 and 3 to get 18.

$$\frac{18}{3}$$

Divide 18 by 3 to get 6.

$$6$$