Solve 1/cos30^circ-tan30^circ=

$$\frac { 1 } { \cos 30 ^ { \circ } } - \tan 30 ^ { \circ } =$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

The square of \sqrt{3} is 3.

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

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

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

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

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