Solve frac{sqrt{3}}{tan60^circ-cos30^circ}-(27)^frac{1{3}}

$$\frac { \sqrt { 3 } } { \tan 60 ^ { \circ } - \cos 30 ^ { \circ } } - ( 27 ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$-1$$

Solution Steps

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

$$\frac{\sqrt{3}}{\sqrt{3}-\cos(30)}-27^{\frac{1}{3}}$$

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

$$\frac{\sqrt{3}}{\sqrt{3}-\frac{\sqrt{3}}{2}}-27^{\frac{1}{3}}$$

Combine \sqrt{3} and -\frac{\sqrt{3}}{2} to get \frac{1}{2}\sqrt{3}.

$$\frac{\sqrt{3}}{\frac{1}{2}\sqrt{3}}-27^{\frac{1}{3}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\frac{1}{2}\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}\sqrt{3}}{\frac{1}{2}\left(\sqrt{3}\right)^{2}}-27^{\frac{1}{3}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}\sqrt{3}}{\frac{1}{2}\times 3}-27^{\frac{1}{3}}$$

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

$$\frac{3}{\frac{1}{2}\times 3}-27^{\frac{1}{3}}$$

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

$$\frac{3}{\frac{3}{2}}-27^{\frac{1}{3}}$$

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

$$3\times \frac{2}{3}-27^{\frac{1}{3}}$$

Multiply 3 and \frac{2}{3} to get 2.

$$2-27^{\frac{1}{3}}$$

Calculate 27 to the power of \frac{1}{3} and get 3.

$$2-3$$

Subtract 3 from 2 to get -1.

$$-1$$