Solve sqrt{3}-1/cos(30^circ)

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

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

Solution Steps

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

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

Divide 1 by \frac{\sqrt{3}}{2} by multiplying 1 by the reciprocal of \frac{\sqrt{3}}{2}.

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

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

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

The square of \sqrt{3} is 3.

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

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

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